When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. Draw a free-body diagram of the person during the jump.

What is the acceleration, as a multiple of g, if this force is applied to a 110 kg bicyclist? This is the combined mass of the cyclist and the bike.

If a car stops suddenly, you feel 'thrown forward.' We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold onto. Describe what happens to you as the car slows down.

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$-kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What was its acceleration (in m/s² and in g's), assumed to be constant, during the crash?

An astronaut is inside a $2.25\times {10}^6$ kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound ($331$ m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than $4g$. What is the maximum initial thrust this rocket's engines can have but just barely avoid blackout? Start with a free-body diagram of the rocket.

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. Draw two free-body diagrams: one for each block.

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$-kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight.

Problems 35, 36, 37, 38, 39, and 40 show a free-body diagram. For each: Identify the direction of the acceleration vector a and show it as a vector next to your diagram. Or, if appropriate, write a = 0.