A cart is moving with a constant horizontal velocity of 5.00 m/s.A small pebble is launched from the front of the cart with a velocity of 8.00 m/s at 60.0° above the horizontal as measured relative to the cart (see figure)and experiences no significant air resistance.Just as the pebble returns to the level from which it was launched,its distance from the front of the cart is closest to
A)2.83 m.
B)4.60 m.
C)5.66 m.
D)9.19 m.
E)11.3 m.

Question

A cart is moving with a constant horizontal velocity of 5.00 m/s.A small pebble is launched from the front of the cart with a velocity of 8.00 m/s at 60.0° above the horizontal as measured relative to the cart (see figure)and experiences no significant air resistance.Just as the pebble returns to the level from which it was launched,its distance from the front of the cart is closest to 
A)2.83 m. 
B)4.60 m. 
C)5.66 m. 
D)9.19 m. 
E)11.3 m.

Quizplus · Accepted Answer

Since the horizontal velocity of the cart is constant, the horizontal motion of the pebble is also constant. Thus, the time it takes for the pebble to return to the level from which it was launched is the same as the time it takes for the pebble to reach its maximum height. We can use the kinematic equation for vertical motion to find this time:
Δy = v0y*t + 0.5*a*t^2
where Δy = 0 (since the pebble returns to its original height), v0y = 8*sin(60) = 6.93 m/s, a = -9.81 m/s^2 (acceleration due to gravity), and we are solving for t:
0 = 6.93*t - 0.5*9.81*t^2
Solving for t gives t = 1.41 s.

During this time, the pebble also moved horizontally with a constant velocity of 5.00 m/s. Therefore, the distance it traveled horizontally is:
Δx = v0x*t
where v0x = 8*cos(60) + 5.00 = 8.50 m/s (initial horizontal velocity of the pebble relative to the ground). Plugging in the value for t, we get:
Δx = 8.50*1.41 = 11.99 m.

The distance from the front of the cart to the pebble when it returns to its original height is the same as the horizontal distance it traveled, so the closest answer choice is C) 5.66 m.

A Cart Is Moving with a Constant Horizontal Velocity of 5.00