An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at \( +13.0 \, \text{m/s}^2 \). At \( t_1 \), the rocket engine is shut down and the sled moves with constant velocity \( v \) until \( t_2 \). The total distance traveled by the sled is \( 5.30 \times 10^3 \, \text{m} \) and the total time is \( 90.0 \, \text{s} \).
Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored?
A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2. Through what angle does the pulley turn in 5.26 s?
A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?
A simple pendulum consists of a sphere tied to the end of a string of negligible mass. The sphere is pulled back until the string is horizontal and then released from rest. Assume the gravitational potential energy is zero when the sphere is at its lowest point.
What angle will the string make with the horizontal when the kinetic energy and the potential energy of the sphere-Earth system are equal?
The International Space Station has a mass of 4.2 x105 kg and orbits Earth at a distance of 4.0 x102 km above the surface. Earth has a radius of 6.37 x106 m, and mass of 5.97 x1024 kg. Calculate the following:
A solid sphere of mass [katex] 1.5 \, \text{kg} [/katex] and radius [katex] 15 \, \text{cm} [/katex] rolls without slipping down a [katex] 35^\circ[/katex] incline that is [katex] 7 \, \text{m} [/katex] long. Assume it started from rest. The moment of inertia of a sphere is [katex] I= \frac{2}{5}MR^2 [/katex].
A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius R.
Using only work and energy, find the velocity of the masses after they have traveled 0.8 meters. Refer to the image above.
A 1100 kg car accelerates from 32 m/s to 8.0 m/s in 4.0 sec. What amount of force was needed to slow it down?
From the figure above, determine the which characteristic fits this collision best.
Find the escape speed from a planet of mass 6.89 x 1025 kg and radius 6.2 x 106 m.
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