Its vertical acceleration is g because the force of gravity is downward. Its horizontal acceleration is zero because no horizontal force acts on it.
A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration?
The minimum speed of a projectile occurs at the top of its path. If it is launched vertically, its speed at the top is zero. If it is projected at an angle, the vertical component of velocity is still zero at the top, leaving only the horizontal component.
At what point in its path does a projectile have minimum speed?
10 m/s to the north
Which of these expresses a vector quantity?
10 kg to the north
10 m/s to the north
An ultra-light aircraft traveling north at 40 km/h in a 30-km/h crosswind (at right angles) has a groundspeed of
Equal horizontal and vertical components.
A ball launched into the air at 45° to the horizontal initially has
equal horizontal and vertical components.
components that do not change in flight.
components that affect each other throughout flight.
a greater component of velocity than the vertical component.
When no air resistance acts on a fast-moving baseball, its acceleration is
due to a combination of constant horizontal motion and accelerated downward motion.
opposite to the force of gravity.
at right angles.
When no air resistance acts on a projectile, its horizontal acceleration is
at right angles to g.
the same as the time going upward.
Without air resistance, the time for a vertically tossed ball to return to where it was thrown is
10 m/s for every second in the air.
the same as the time going upward.
less than the time going upward.
more than the time going upward.
Scalar quantity has no direction, only magnitude. Vector quantities have direction and magnitude.
How does vector quantity differ from a scalar?
Velocity is by convention a vector quantity, so has a direction associated with it. Speed is Simply the magnitude of the velocity, and hence is just a number, so is a scalar.
For example, if you were walking from the origin at 5mph down the negative x-axis, your speed would be 5mph, but your velocity would be -5mph, as you are walking in the negative direction.
Why a speed a scalar quantity but velocity a vector quantity?
If a vector that is 1 cm long represents a velocity of 10 km/h, what velocity does a vector 2 cm long?
The length of the diagonal. It doesn’t need to be a rectangle so long as the lines are drawn to scale and are pointing at the same angle as the actual velocities. The angle and distance represent the effective angle and velocity.
When a rectangle is constructed in order to add velocities, what represents the resultant of the velocities?
Because a rectangle is just a paralellogram with right angle
Why do we say a rectangle is a special case of a parallelogram?
Larger. Just remember the Pythagorean theorem. When you draw a right triangle, the vector will be the hypotenuse. Since it’s a 45 degree angle, the vertical and horizontal components are equal. The vector will be larger than them by a factor of square root of 2.
Will a vector at 45° to the horizontal be larger or smaller than its horizontal and vertical components?
There is no horizontal component of force
Why does a bowling ball move without acceleration when it rolls along a bowling alley?
There is no horizontal component of gravitational force
In the absence of air resistance, why does the horizontal component of velocity for a projectile remain constant while the vertical component changes?
Same; both are under the influence of gravity
How does the downward component of the motion of a projectile compare with the motion of free fall?
They hit the ground at the same time. The same force of gravity is acting on both balls. Since both balls started falling (from the force of gravity) from the same height, they will fall towards the ground with the same acceleration.
At the instant a ball is thrown horizontally over a level range, a ball held at the side of the first is released and drops to the ground. If air resistance is neglected, which ball strikes the ground first?
a. d = 1/2 a t^2
… where d is distance, a is acceleration, and t is time.
So in this case, t=1 second, and a=9.8 m-sec^-2, so d must be 4.9 meters.
b. Initial speed is irrelevant as long as projectile flies for more than one second. The gravity always pulls the projectile the same.
a. How far below an initial straight-line path will a projectile falling one second?; b. Does your answer depend on the angle of launch or on the initial speed of the projectile? Defend your answer.
Straight up; 45°
At what angle should a slingshot be oriented for maximum altitude? For maximum horizontal range?
Neglecting air resistance, if you throw a ball straight up with a speed of 20 m/s, how fast will it be moving when you catch it?
a. Equal to b. yes, it decreases
a. Neglecting air resistance, if you throw a baseball at 20 m/s to your friend who is on first base, will the catching speed be greater than, equal to, or less than 20 m/s?; b. does the speed change if air resistance is a factor?
A satellite. The moon is a natural satellite, and there are many many artificial satellites. It traveling fast enough to fall around Earth rather than into it
What do we call a projectile that continually “falls” around Earth?
Since the satellite moves at 8 km/s, it “falls” at the same rate Earth “curves.”
How fast must a projectile moving horizontally travel so that the curve it follows matches the curve of Earth?
To avoid the heating effects of atmospheric friction
Why is it important that such a satellite be above Earth’s atmosphere?
What force acts on a satellite that is above Earth’s atmosphere?
200 km/h + 50 km/h = 250 km/h; 100 km/h – 10 km/h = 150 km/h
Calculate the resultant velocity of an airplane that normally flies at 200 km/h if it encounters a 50-km/h tailwind. If it encounters a 50-km/h headwind.
100 km/h – 75 km/h = 25 km/h N; 100 km/h + 75 km/h= 175 km/h N
Calculate the resultant of the pair of velocities 100 km/h north and 75 km/h south. Calculate the resultant if both of the velocities are directed north.
√[(100 km/h)2 + (100 km/h)2] = 141 km/h at 45° to either vector
Calculate the magnitude of the resultant of a pair of 100-km/h velocity vectors that are at right angles to each other.
sin(theta) = opposite/hypotinuse
cos(theta) = adjacent/hypotinuse
sin(45) = y/100
100sin45 = y
y = 100(squr(2)/2)
cos(45) = x/100
100cos45 = x
x = 100(squr(2)/2)
Take note that at 45 degrees, the x and y components are equal (initially). This is because 45 degrees is the halfway mark between a purely horizontal motion (0 degrees) and vertical motion (90 degrees).
Calculate the magnitude of the horizontal and vertical components of a vector that is 100 units long and is oriented at 45°.
Resultant = √(42 + 32) = 5. This is the hypotenuse of a 3-4-5 right triangle.
Calculate the resultant of a horizontal vector with a magnitude of 4 units and a vertical vector with a magnitude of 3 units.
5 is hypotenuse; 3 is opposite 37°, 4 is opposite 53°
A right triangle with sides of 3, 4 and 5 units has angles that are 37°, 53°, and 90° respectively. Which of its sides is the hypotenuse? Which side is oppose the 37° angle? Which side is opposite the 53° angle?
Horizontal, 4/5 x 10 = 8; vertical 3/5 x 10 = 6 (twice the sides of the 3-4-5 triangle)
What are the horizontal and vertical components of a 10-unit vector that is oriented 37° above the horizontal?
Horizontal, 3/5 x 10 = 6, vertical 4/5 x 10 = 8
What are the horizontal and vertical components of a 10-unit vector that is oriented 53° above the horizontal?
Vertical 4/5 x 20 = 16 m/s; horizontal, 3/5 x 20 = 12 m/s; horizontal; vertical
The launching velocity of a projectile is 20 m/s at 53° above the horizontal. What is the vertical component of its velocity at launch? Its horizontal component of velocity? Neglecting air friction, which of these components remains constant throughout the flight path? Which of these components determines the projectile’s time in the air?
8 km/s x 1 mi / 1.6 km x 3600 s / 1 h = 18,000 mi/h
Satellites in a circular, low Earth-orbit move at 8-km/s. Convert this speed to miles per hour. (there are about 1.6 km in 1 mile and 3600 s in 1 h.
When vectors are aligned and in the same direction 4 + 5=9 units; when vectors oppose each other 5 – 4 = 1 unit
What is the maximum possible resultant of two vectors with magnitudes of 4 and 5 units? What is the minimum possible resultant?
Yes, the diagonal of any rectangle is greater than either of it sides
If you swim in a direction directly across a river and you end up downstream due to the flow of water, do you move faster than you would if the water didn’t flow? Explain.
No acceleration; air resistance balances the weight of the raindrops and the raindrops have reached terminal speed
The speed of falling rain is the same 10 m above the ground as it is just before it hits the ground. What does this tell you about whether or not the rain encounters air resistance?
Rain falling vertically will make vertical streaks on a car’s side window. However, if the car is moving, the streaks are slanted. If the streaks from a vertically falling rain make 45 degree streaks
Rain falling vertically will make vertical streaks on a car’s side window. However if the car is moving, the streaks are slanted. If the streaks from a vertically falling rain make 45° streaks, how fast is the car moving compared with the speed of the falling rain?
The distance increases because the component of your velocity along the road decreased slightly while there was a component across the road while you changed lanes.
The “hang time” depends on the vertical velocity when you jump. Because the acceleration of gravity acts in the vertical, not in the horizontal.
The horizontal speed will effect the distance that your feet are off the ground, but not the time.
You’re driving behind a car and wish to pass, so you turn to the left and pull into the passing lane without changing speed. Why does the distance increase between you and the car you’re following?
If it is launched straight up, it is not moving at all at the absolute top of its trajectory. But the acceleration of gravity quickly makes it start falling. At 45 degrees, it will have no vertical speed, but it will have horizontal speed and it will be 141(cos 45) or 99.7 m/s.
A projectile is launched straight up at 141 m/s. How fast is it moving at the top of its trajectory? Suppose it is launched upward at 45° above the horizontal plane. How fast is it moving at the top of its curved trajectory?
Only on the vertical component of velocity as your feet leave the ground. Once off the ground the only acceleration (neglecting any effects of air drag) is g, which is vertical. Your liftoff velocity divided by g will be the time you move upward. Double this and you have your hang time.
When you jump up, your hang time is the time your feet are off the ground. Does hang time depend on your vertical component of velocity when you jump, your horizontal component of velocity, or both? Defend your
Horizontal distance makes no difference in this problem. the hang time will be the same as before (2/3 seconds).
The hang time of a basketball player who jumps a vertical distance of 2 feet (0.6 m) is 2/3 second. What will be the hang time if the player reaches the same height while jumping a horizontal distance of 4 feet (1.2 m)?
8km/s is the orbital speed for low earth orbit; this means that the projectile is moving fast enough, that for every meter it falls toward the center of the earth, it moves “forward” fast enough that the curvature of the earth slips away by 1 meter…so that the distance between the projectile and surface of the earth remains constant…and the projectile never hits the earth…
If it traveled slower than this, it would eventually hit the earth
Assuming no air resistance, why does a projectile launched horizontally at 8 km/s not strike earth’s surface?
It falls beneath the straight-line tangent it would follow if gravity were not acting on it
We think of something falling if it gets closer to the ground. Yet a satellite in circular orbit does not get closer to the ground, because Earth curves as much as the satellite’s trajectory does. So how can we say it falls? (Hint: compare the position of the satellite with the imaginary line it would follow if there were not gravity. Does it fall below this line?)
As Harry took 4 Seconds to reach the swimming pool the helicopter also must have travelled 4 seconds horizontally. Its horizontal velocity is already given, 110 m/s. So the distance travelled is the product of velocity and time. Hence, the dist. bet. Harry and swimming pool at the begennin of the fall is equal to 110 x 4 = 440 metres.
Harry accidentally falls out of a helicopter that is traveling at 110 m/s. He plunges into a swimming pool 4s
The pellet’s vertical velocity was zero the as it travels toward the target, it accelerates vertically because of the earth’s gravity.
s = 1/2a t^2
s = 1/2 * 9.8 * 0.5 ^2
s = 1.25 meters above the target
A girl throws a slingshot pellet directly at a target that is far enough to take one half second to reach. How far below does the target hit? How hight above the target should she aim?
First figure out how many seconds it would take for the crate to fall 125 m, then relate it to the 50 m/s. You can do this.
A shiny new sports car sits in the parking lot of a dealership. Above is a cargo plane, flying horizontally at 50 m/s. At the exact moment the plane is 125 m directly above the car, a heavy crate accidentally falls from its cargo doors. Relative to the car, where will the crate hit?