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

Using the equation for impulse: 
Impulse = Change in momentum

We can find the impulse by first finding the momentum of the stone at the highest point of its trajectory. At this point, the velocity of the stone is 0 m/s, so its momentum is also 0.

Next, we can use the conservation of energy to find the initial velocity of the stone.

Potential energy at the highest point = Kinetic energy at the initial point

mgh = (1/2)mv^2

Solving for v, we get:

v = sqrt((2gh)/m) 
   = sqrt((2 x 9.81 x 34.3)/0.28) 
   = 19.5 m/s

The initial momentum of the stone is:

p = mv = 0.28 x 19.5 = 5.46 kg m/s

Finally, the impulse is the change in momentum, which is:

Impulse = p_final - p_initial 
         = -p_initial (Because the final momentum is 0) 
         = -(5.46) 
         = -5.46 N s

Since the stone is traveling upwards, the impulse is in the opposite direction (downwards) and has a magnitude of 5.46 N s. However, the options only provide positive values, so we choose the closest option, which is C) 7.3 N s, upwards (rounded to one significant figure).

A 028-Kg Stone You Throw Rises 34