A ball of mass 0,2kg travels towards a hockey player at 10 m.s-1.A force of 350N is exerted on the ball when she hits it so that it travels at 7,5 m.s-1 in the opposite direction.Calculate the time that the ball was in contact with the hockey stick
To calculate the time that the ball was in contact with the hockey stick, we can use the principle of impulse-momentum.
The impulse on an object is equal to the change in momentum. Momentum is defined as the product of mass and velocity.
The initial momentum of the ball can be calculated as follows:
Initial momentum = mass x initial velocity
= 0.2 kg x 10 m/s
= 2 kg·m/s
The final momentum of the ball can be calculated as follows:
Final momentum = mass x final velocity
= 0.2 kg x (-7.5 m/s) [since the ball travels in the opposite direction]
= -1.5 kg·m/s
The change in momentum can be calculated as follows:
Change in momentum = Final momentum - Initial momentum
= -1.5 kg·m/s - 2 kg·m/s
= -3.5 kg·m/s
Now, we know that impulse is equal to the force applied multiplied by the time duration of the force. So we can write:
Impulse = Force x time
In this case, the impulse exerted on the ball is equal to the change in momentum. Therefore, we can write:
Impulse = Change in momentum
Substituting the values we have:
350 N x time = -3.5 kg·m/s
Now, we can solve for time:
time = (-3.5 kg·m/s) / 350 N
time = -0.01 s
The negative sign indicates that the ball was in contact with the hockey stick for a very short duration, of 0.01 seconds, which is in the opposite direction to the ball's initial velocity.