Some kid (mass 20 kg) jumps with a velocity of 3.2 m/s horizontally off some steps (height 0.55 m) onto his heavy duty skateboard (mass 3 kg, height 0.03 m), which is initially at rest. How fast will he be skating?
Need to find initial momentum and final momentum. So, initial momentum is mass of kid times their velocity plus the mass of skateboard times its initial velocity(vi=0). Therefore, Pi=(20)(3.2)+(3)(0). Final momentum equals the mass of the kid times its final velocity (which is unknown) plus the mass of skateboard times its final velocity (also unknown). So, Pf=(20+3)vf. Solve for vf by setting Pi equal to Pf due to momentum conservation. (20)(3.2)+(3)(0)=(20+3)vf. Final velocity turns out to be 2.783 m/s
To find the speed of the kid after he jumps onto the skateboard, we can apply the law of conservation of momentum.
The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces act on the system. The momentum of an object is calculated by multiplying its mass by its velocity.
Before the kid jumps onto the skateboard, both the kid and the skateboard are at rest, so their initial momentum is zero.
After the kid jumps onto the skateboard, the total momentum of the system (kid + skateboard) will be the sum of their individual momenta. Let's calculate their individual momenta first.
The momentum of the kid (p_kid) can be calculated using the equation:
p_kid = mass_kid * velocity_kid
Given that the mass of the kid (mass_kid) is 20 kg and the velocity of the kid (velocity_kid) is 3.2 m/s, we can calculate the momentum of the kid.
p_kid = 20 kg * 3.2 m/s
= 64 kg·m/s
Next, let's calculate the momentum of the skateboard (p_skateboard). Since it is initially at rest, its momentum will also be zero.
p_skateboard = 0 kg * 0 m/s
= 0 kg·m/s
Now, let's find the total momentum of the system after the jump by summing up the individual momenta:
Total momentum = p_kid + p_skateboard
= 64 kg·m/s + 0 kg·m/s
= 64 kg·m/s
According to the law of conservation of momentum, this total momentum after the jump will be the same as the total momentum before the jump (which is zero).
Now, let's calculate the speed of the kid and skateboard together (v_final). We know that the combined mass of the kid and the skateboard (mass_total) is the sum of their individual masses.
mass_total = mass_kid + mass_skateboard
= 20 kg + 3 kg
= 23 kg
Using the equation for momentum, we can solve for the final velocity of the kid and skateboard:
Total momentum = mass_total * v_final
v_final = Total momentum / mass_total
= 64 kg·m/s / 23 kg
= 2.78 m/s (rounded to two decimal places)
Therefore, the kid will be skating at a speed of approximately 2.78 m/s after jumping onto the skateboard.