Question

For the same force, why does a long cannon impart more speed to a cannonball than a short cannon?

The kinetic energy of an object of mass 2 kg is 16 J. What is its linear momentum?

A 70.0 kg archer, standing on frictionless ice, shoots an 80.0 g arrow at a speed of 80 m/s. What is the recoil speed of the archer?

Explain two ways by which you can increase the impulse.   

Answer 1

Answer-1 In long cannon, the cannonball will receive more momentum due to force acting for more time in the long cannon.So for the same force, long cannon impart more speed than the short cannon to a cannonball.

Answer-2 Since kinetic energy is given,K.E=16 ,we know kinetic energy is given by K.E=1/2mv.v, also mass is given,M=2kg.so 16=1/2*mass*velocity*velocity 32=2kg*velocity*velocity so velocity=4 now linear momentum is given by=mass*velocity.SO Momentum=2*4=8(kg⋅m/s).

Answer-3 Momentum is coserved here due to frictionless ice.M1V1 + m1v1 = M2V2 + m2v2

Since before the archer shoots the arrow, the arrow and the archer weren't moving so V1 and v1 are zero.
0 = M2V2 + m2v2.
M2V2 = -m2v2
V2 = -m2/M2 * v2

V2=- 0.08/70*80=0.09m/s

so recoil speed of archer is -0.09m/s.

Answer-4 two ways to increase the impulse. 1)Increase the force and 2)Increase the time interval.