A frictionless ski jump is designed such that at the bottom of the hill, there is a short flat section. After the flat section, the slope continues into a ramp of vertical height 0.08 m, at an angle 40 degrees (relative to the horizontal). The top of the ski jump is 475 m high off the ground. Block A of mass 19kg is released from the top of the slope so that it slides down and makes a perfectly elastic collision with Block B of mass 8.93kg. This causes the Block B to slide up the frictionless ramp and undergo projectile motion, before landing a horizontal distance x m away from the ramp. MA Part 1 тв Ꮎ x What is the speed of Block B (in m/s), immediately after the perfectly elastic collision? VB = number (rtol=0.05, atol=1e-08) m/s ? Part 2 What is the horizontal distance (in m) that Block B travels after it goes off the ramp (x)? x = number (rtol=0.05, atol=1e-08) m

A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 3.0 m/s, what is the maximum mass of grain that it can accept?

Two projectiles of mass m1 and m2 , are fired at the same speed but in opposite directions from two launch sites separated by a distance D. They both reach the same spot in their highest point and strike there. As a result of the impact they stick together and move as a single body afterwards. Find the place they will land.

Check Your Understanding Even if there were some friction on the ice, it is still possible to use conservation of momentum to solve this problem, but you would need to imposed an additional condition on the problem. What is that additional condition?

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?

What is the average momentum of an avalanche that moves a 40-cm-thick layer of snow over an area of 100 m by 500 m over a distance of 1 km down a hill in 5.5 s? Assume a density of 350kg/m3 for the snow.

The coefficient of friction between the block of mass ml = 3.00 kg and the surface in Figure P7.22 is k = 0.400. The system starts from rest. What is the speed of the ball of mass, m2 = 5.00 kg when it has fallen a distance h = 1.50 m? Figure P7.22

A projectile of mass 2.0 kg is fired in the air at an angle of 40.0 to the horizon at a speed of 50.0 m/s. At the highest point in its flight, the projectile breaks into three parts of mass 1.0 kg, 0.7 kg, and 0.3 kg. The 1.0-kg part falls straight down after breakup with an initial speed of 10.0 m/s, the 0.7-kg part moves in the original forward direction, and the 0.3-kg part goes straight up. Launch a. Find the speeds of the 0.3-kg and 0.7-kg pieces immediately after the break-up. b. How high from the break-up point does the 0.3-kg piece go before coming to rest? c. Where does the 0.7-kg piece land relative to where it was fired from?

In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assuming that the mass of the drivers is much, much less than that of the bumper cars, what are their final speeds?

A proton traveling at 3.0106m/s scatters elastically from an initially stationary alpha particle and is deflected at an angle of 85 with respect to its initial velocity. Given that the alpha particle has four times the mass of the proton, what percent of its initial kinetic energy does the proton retain after the collision?