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

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.

Quizplus · Accepted Answer

We can use the impulse-momentum theorem, which states that the impulse applied to an object is equal to its change in momentum. In this case, the stone starts at rest and reaches a certain velocity at the highest point of its trajectory, where it stops momentarily before falling back down. Therefore, we can calculate the momentum of the stone at its highest point as:

p = m * v

where m is the mass of the stone and v is its velocity at its highest point, which is zero. Therefore, the momentum of the stone at its highest point is zero.

Since the impulse applied to the stone is equal to its change in momentum, we can calculate the impulse as:

J = Δp = p_f - p_i = 0 - m * v_i

where v_i is the initial velocity of the stone when it is thrown. We don't know the value of v_i, but we can use the fact that the stone rises 34.3 m to find it. Using the kinematic equation for vertical motion, we have:

Δy = v_i * t - 0.5 * g * t^2

where Δy is the vertical displacement, t is the time of flight, and g is the acceleration due to gravity. Plugging in the given values, we have:

34.3 = v_i * t - 0.5 * 9.81 * t^2

Solving for t, we get:

t = 3.13 s

Plugging this value back into the equation and solving for v_i, we get:

v_i = 10.6 m/s

Finally, we can calculate the impulse as:

J = 0 - m * v_i = -0.28 kg * 10.6 m/s = -2.968 Ns ≈ -2.97 Ns

Since the impulse is negative, that means it is directed downwards, which corresponds to choice C.

A 028-Kg Stone You Throw Rises 34