A child is trying to throw a ball over a fence.She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the horizontal.The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high.The ball just clears the fence while still traveling upwards..How far is the child from the fence if you neglect air?
A)0.73 m
B)1.6 m
C)2.7 m
D)3.8 m
E)7.5 m

Question

Quizplus · Accepted Answer

Firstly, we need to find the maximum height the ball reaches. We can use the formula:
H = (V^2 sin^2θ) / 2g
where V is the initial velocity (8.0 m/s), θ is the angle above the horizontal (40°), and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get:
H = (8.0^2 sin^2(40°)) / (2*9.8) = 1.91 m

Since the ball just clears the fence while still traveling upwards, we know that its height at that point is equal to the height of the fence (2.0 m). Therefore, we can use the same formula to find the horizontal distance traveled by the ball before reaching that height. This time, we want to find the distance traveled (x) instead of the maximum height, so we rearrange the formula:
x = (V^2 sin(2θ)) / g
Plugging in the values, we get:
x = (8.0^2 sin(2*40°)) / 9.8 = 1.6 m

Therefore, the child is 1.6 m from the fence. Hence, the answer is B.

A Child Is Trying to Throw a Ball Over a Fence.She