Prepare a before-and-after visual overview for these problems, but do not solve
ID: 1523547 • Letter: P
Question
Prepare a before-and-after visual overview for these problems, but do not solve them. Draw pictures of "before" and "after." Establish a coordinate system. Define symbols relevant to the problem. List known information, and identify the desired unknown. A 50 kg archer, standing on frictionless ice, shoot a 100 g arrow at a speed of 100 m/s. what is the recoil speed of the archer? The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1 mph. toward a group of small innocent children. As you see the situation, you realize there is just time for you to drive your 1000 kg Volkswagen head-on into the Cadillac and thus save the children. With what speed should you impact the Cadillac to bring it to a halt? Dan is gliding on his skateboard at 4 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8 m/s. How fast is Dan going as his feet hit the ground? Dan's mass is 50 kg and the skateboard's mass is 5 kg.Explanation / Answer
9)
Mass of the Archer (mA) = 50 kg
Mass of arrow (ma) = 100 grams = 0.100 kg
Initial Velocity of the Archer (UA) = 0 m/s
Initial Velocity of the arrow (Ua) = 0 m/s
Final Velocity of the Archer (VA) = Unknown
Final Velocity of the arrow (Va) = 100 m/s
All the initial velocities are zero, so the whole left side of the equation becomes zero.
0 = ma * Va + mA * VA
Now we have one unknown, we can solve for VA
VA = - (ma * Va) / mA
VA = - (0.100 kg * 100 m/s) / 50 kg
VA = - 0.200 m/s
The minus sign indicates that the Archer's final velocity is in the opposite direction as the velocity of the arrow.
10)
Sum of momenta = 0( Since both the cars stop)
Let m1 be the mass of the cadillac and m2 be the mass of the volkswagen.
then, v1 = speed of cadillac and v2 = speed of volkswagen.
Therefore, (m1)*(v1) + (m2)*(v2) = 0
Substituting,
(2000*1) + (1000*v2) = 0
2000 = - 1000 v2
Therefore, v2= - 2 mph.
11)
Momentum is always conserved so momentum before = momentum after.
So (m1 x u1) + (m2 x u2) = (m1 x v1) + (m2 x v2)
(50 x 4) + (5 x 4) = (50v) + (5 x 8)
50v = (200 + 20) - 40
v = 180/50
v = 3.6 m/s