A 0.28-kg stone you throw rises 34.3 m in the air.The impulse the stone receives from your hand while being thrown is
A)2.7 N . s,up.
B)2.7 N . s,down.
C)7.3 N . s,up.
D)7.3 N . s,down.
E)9.6 N . s,up.

Question

Quizplus · Accepted Answer

Using the kinematic equation: 
Δy = viΔt + (1/2)at^2
We know that at the highest point, the final velocity (vf) is zero, the initial velocity (vi) is what we're trying to find, acceleration is acceleration due to gravity (-9.8 m/s^2), and the displacement (Δy) is 34.3 m.
So, we have: 
0 = vi - 9.8t
t = vi/9.8
Δy = vi/9.8 * vi/2
Solving for vi, we get: 
vi = √(2 * Δy * 9.8)
vi = √(2 * 34.3 * 9.8) ≈ 18.7 m/s
Now, impulse (J) is given by: 
J = FΔt
Since the stone starts and ends at rest, we know that impulse equals the change in momentum: 
J = Δp = mvf - mvi
J = (0 - mv) - (mv - 0) = -2mv
J = -2(0.28 kg) * 18.7 m/s ≈ -9.9 Ns (Note that the negative sign just tells us that the impulse is in the opposite direction of the motion of the stone)
Since the question asks for magnitude, we can take the absolute value: 
|J| ≈ 9.9 Ns (rounding to one significant figure)
The only answer choice that is closest to this value is (C) 7.3 Ns up.

A 028-Kg Stone You Throw Rises 34