Practice 1.3A Solutions
Horizontal Projectiles
Multiple Choice
1.
An object slides off a roof 10 meters above the ground with an initial horizontal speed of 5 meters per second as
shown above. The time between the object's leaving the roof and hitting the ground is most nearly
Answer: C For a horizontal projectile; h = ½ gt2 (initial vertical component of velocity is zero)
2.
A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the
water a distance d from the base of the cliff. How far from the base of the cliff would the diver have landed
if the diver initially had been moving horizontally with speed 2v?
(A) d (B) 2d (C) 2d (D) 4d (E) can’t be determined without knowing the height of the cliff
The time in the air for a horizontal projectile is dependent on the height and independent of the
initial speed. Since the time in the air is the same at speed v and at speed 2v, the distance (d = vt)
will be twice as much at a speed of 2v
3.
4.
Robin Hood aims his longbow horizontally at a target's bull's eye 30 m away. If the arrow strikes the target
exactly 1.0 m below the bull's eye, how fast did the arrow move as it was shot from the bow? Assume air
resistance is negligible.
(A) 6.0 m/s (B) 13 m/s (C) 33 m/s (D) 67 m/s (E) 150 m/s
For a horizontal projectile (viy = 0 m/s) to fall 1 m takes (using 1 m = ½ gt2) 0.45 seconds. To
travel 30 m in this time requires a speed of d/t = (30 m)/(0.45 s)
A flare is dropped from a plane flying over level ground at a velocity of 70 m/s in the horizontal direction.
At the instant the flare is released, the plane begins to accelerate horizontally at 0.75 m/s 2. The flare takes
4.0 s to reach the ground. Assume air resistance is negligible. Relative to a spot directly under the flare at
release, the flare lands
(A) directly on the spot. (B) 6.0 m in front of the spot. (C) 274 m in front of the spot. (D) 280 m in front of
the spot. (E) 286 m in front of the spot.
Answer: D
In the 4 seconds to reach the ground, the flare travelled 70 m/s × 4 s = 280 m horizontally.
5.
As seen by the pilot of the plane (in question #41) and measured relative to a spot directly under the
plane when the flare lands, the flare lands
(A) 286 m behind the plane. (B) 6.0 m behind the plane. (C) directly under the plane. (D) 12 m in front of
the plane. (E) 274 m in front of the plane
In the 4 seconds to reach the ground, the flare travelled 70 m/s × 4 s = 280 m horizontally. The
plane travelled d = vit + ½ at2 = (70 m/s)(4 s) + (0.5)(0.75 m/s2)(4 s) = 280 m + 6 m, or 6 m ahead of
the flare.
The free fall trajectory of an object thrown horizontally from the top of a building is shown as the dashed
line in the figure. Which sets of arrows best correspond to the directions of the velocity and of the
acceleration for the object at the point labeled P on the trajectory?
2
6.
Answer: A
Velocity is pointing tangent to the path, acceleration (gravity) is downward.
During a recent winter storm, bales of hay had to be dropped from an airplane to a herd of cattle below. Assume
the airplane flew horizontally at an altitude of 180 m with a constant velocity of 50 m/s and dropped one bale of
hay every two seconds. It is reasonable to assume that air resistance will be negligible for this situation.
7.
As the bales are falling through the air, what will happen to their distance of separation?
(A) the distance of separation will increase
(B) the distance of separation will decrease
(C) the distance of separation will remain constant
(D) the distance of separation will depend on the mass of the bales
(E) none of the above are always true
As the first bales dropped will always be traveling faster than the later bales, their relative velocity will cause their
separation to always increase.
8.
About how far apart from each other will the bales land on the ground?
(A) 9000 m (B) 300 m (C) 180 m (D) 100 m (E) 50 m
Horizontally, the bales will all travel at the speed of the plane, as gravity will not affect their horizontal
motion. D = vt = (50 m/s)(2 seconds apart)
Free Response
Problem 1
A golfer practicing on a range with an elevated tee 4.9 m above the fairway is able to strike a ball so that
it leaves the club with a horizontal velocity of 20 m s–1. (Assume the acceleration due to gravity is 9.80
m s–2, and the effects of air resistance may be ignored unless otherwise stated.)
a)
b)
c)
d)
e)
How long after the ball leaves the club will it land on the fairway?
What horizontal distance will the ball travel before striking the fairway?
What is the acceleration of the ball 0.5 s after being hit?
Calculate the speed of the ball 0.80 s after it leaves the club.
With what speed will the ball strike the ground?
Problem 2 Solution
Problem 2
An emergency relief plane is dropping a care package from a plane to a group of medical personnel
working for a relief agency in an African village. The package is designed to land in a small lake,
inflate an attached raft upon impact, and finally resurface with the raft side down. The plane will be
moving horizontally with a ground speed of 59.1 m/s. The package will be dropped a horizontal
distance of 521 m from the intended target location. At what altitude above the pond must the plane
be flying in order to successfully accomplish this feat? (381 m)