Two young sisters with a combined mass of 75 kg ride on a cart of mass 30.0kg travelling at 2.0 m/s. If they jump off together so they land with zero speed relative to the ground, what is the change in speed of the cart?
Wrong! The answer has to be 7 m/s. Its just reverse logic. M1Vc + M2Vc = M1V1 + M2V2.
Vc = 2, V1 = 0 (assuming it starts from rest), V2 = unknown, and thats what you are finding.
thank you !
M1 = 75, M2 = 30
To solve this problem, let's use the principle of conservation of momentum. The total momentum before the sisters jump off should be equal to the total momentum after they jump off, assuming no external forces act on the system.
The formula for momentum is given by:
Momentum (p) = Mass (m) × Velocity (v)
Let's calculate the initial momentum before the jump:
The mass of the first sister = m1 = given as 75 kg
The mass of the second sister = m2 = also given as 75 kg
Total initial mass (m_total_initial) = m1 + m2 = 75 kg + 75 kg = 150 kg
The initial velocity of the cart (v_cart_initial) = given as 2.0 m/s
Using the formula for momentum, the initial momentum before the jump is:
Initial momentum (p_initial) = m_total_initial × v_cart_initial
Now, let's calculate the final momentum after the jump:
Since the sisters land with zero speed (relative to the ground), their momentum after the jump will be zero.
The final mass of the system (m_total_final) will be the mass of the cart alone since the sisters have jumped off.
Final velocity of the cart (v_cart_final) = ?
Using the formula for momentum, the final momentum after the jump is:
Final momentum (p_final) = m_total_final × v_cart_final
According to the principle of conservation of momentum:
p_initial = p_final
m_total_initial × v_cart_initial = m_total_final × v_cart_final
To find the change in speed of the cart, let's rearrange the equation:
v_cart_final = (m_total_initial × v_cart_initial) / m_total_final
Substitute the given values:
v_cart_final = (150 kg × 2.0 m/s) / 30.0 kg
Calculating the final velocity:
v_cart_final = 10 m/s
Therefore, the change in speed of the cart is 10 m/s.
Initial momentum=finalmomentum
(2*75+30)2.0=2*75*0+ 30v
solve for velocity v.
then the change is speed is v-2.0