n 80 kg man is riding on a small 40 kg cart at a speed of 4 m/s. He jumps off the cart with zero horizontal speed. The final speed of the cart ______(in m/s).
Question
n 80 kg man is riding on a small 40 kg cart at a speed of 4 m/s. He jumps off the cart with zero horizontal speed. The final speed of the cart ______(in m/s).
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the man jumps is equal to the total momentum after he jumps.
Step 1: Calculate the initial momentum The initial momentum (before the man jumps) is the sum of the momentum of the man and the cart. Momentum is calculated as mass times velocity. So, the initial momentum is:
(80 kg * 4 m/s) + (40 kg * 4 m/s) = 320 kgm/s + 160 kgm/s = 480 kg*m/s
Step 2: Calculate the final momentum After the man jumps, he has zero horizontal speed, so his momentum is 0. The final momentum is then just the momentum of the cart. We'll call the final speed of the cart v. So, the final momentum is:
40 kg * v
Step 3: Set the initial momentum equal to the final momentum According to the principle of conservation of momentum, these two should be equal:
480 kg*m/s = 40 kg * v
Step 4: Solve for v Divide both sides by 40 kg to solve for v:
v = 480 kg*m/s / 40 kg = 12 m/s
So, the final speed of the cart is 12 m/s.
Similar Questions
A 58 kg man is riding on a 60 kg cart traveling at a speed of 1 m/s. He jumps off with zero horizontal speed (relative to the ground). What is the resulting change in the speed of the cart?
A girl of mass 40 kg running with the velocity 2 m/s jumps on a stationary cart of mass 4 kg. Find the velocity of the girl when the cart starts moving
A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4sec his displacement relative to the ground will be
Two carts with masses of 4.40 kg and 2.68 kg move toward each other on a frictionless track with speeds of 5.14 m/s and 3.04 m/s respectively. The carts stick together after colliding head-on. Find the final speed.
A push cart of mass 200 kg is loaded with vegetables of 50 kg initially. A vegetable vendor pushed the cart to the maximum and made it to accelerate by 2m/s22m/s 2 . He sold all the vegetables and on his way home, he pushed the empty cart to the maximum and made it to accelerate. Find the acceleration of the empty push cart.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.