A 20,000 kg rocket has a rocket motor that generates 3.0 x 10⁵ N of thrust. Assume no air resistance. What is the rocket's initial upward acceleration?

A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if: The box moves at a steady 5.0 m/s?

A rocket of mass m is launched straight up with thrust F_thrust. Find an expression for the rocket's speed at height h if air resistance is neglected.

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a 'crumple zone' in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm. A 60 kg person is in a head-on collision. The car's speed at impact is 15 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.

A 500 g model rocket is on a cart that is rolling to the right at a speed of. The rocket engine, when it is fired, exerts an 8.0 N vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the ground. At what horizontal distance left of the hoop should you launch?

As a science fair project, you want to launch an 800 g model rocket straight up and hit a horizontally moving target as it passes 30 m above the launch point. The rocket engine provides a constant thrust of 15.0 N. The target is approaching at a speed of 15 m/s. At what horizontal distance between the target and the rocket should you launch?

Two rock climbers, Paul and Jeanne, use safety ropes of similar length. Jeanne's rope is more elastic, called a dynamic rope by climbers. Paul has a static rope, not recommended for safety reasons. Jeanne (Fig. 4–72) falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m. Estimate how large a force (assume constant) she will feel from the rope. (Express the result in multiples of her weight.)

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A 25-g projectile is fired into a cube of ballistic gel at a velocity of 360 m/s. If the projectile penetrates 15 cm into the gel before stopping, find the average force exerted by the gel onto the projectile. Use kinematics and dynamics (Newton's laws).