Mechanics | Relativity Answers

A plane is flying in a straight line at an unchanging height and unchanging speed. The pilot must drop an object onto a target in front of the plane. At what angle must the pilot see the target at the moment of dropping the object? At that moment, what is the distance between the target and the plane’s projection onto the ground? Disregard air resistance.

The last car unfastens from a moving train. The train continues to move at the same constantspeed. What is the ratio of the paths covered by the train and car up to the moment of the car’s stop? Assume that the car decelerates uniformly. Solve this problem graphically.

The driver notices that the rain leaves no trace on the back windshield of his car slanted at a 60° angle to the horizontal when the car is moving faster than 30 km per hour. Find the velocity of rain droplets.

A wagon with a width of 2.4 m, moving at a speed of 15 m per second, was shot through by a bullet perpendicular to the movement of the wagon. The distance between the two bullet holes in the wagon’s walls is 6 cm. What is the speed of the bullet ?

Find the frequency of a sound wave moving in air at room temperature with a wavelength of
0.667 m.

A 50 g mass attached to a spring, the spring constant of which is 0.49 N/m, oscillates. What
should be the length of a mathematical pendulum for its frequency to equal that of a spring
pendulum?

A 0.73 kg magnetic target is suspended on a string. A 0.025 kg magnetic dart, shot
horizontally, strikes it head on. The dart and the target together swing up 12 cm above the
initial level. What was the initial velocity of the dart?

As everyone knows, bullets bounce from Superman’s chest. Suppose Superman, mass
104 kg, while not moving, is struck by a 4.2 g bullet moving with a speed of 835 m/s. If the
collision is elastic, find the speed that Superman had after the collision. (Assume the
bottoms of his superfeet are frictionless.)

A thread holds two carts together on a frictionless surface as in the figure below. A
compressed spring acts on the carts. After the thread is burned, the 1.5 kg cart moves with
a velocity of 27 cm/s to the left. What is the velocity of the 4.5 kg cart?

A 4.00 kg model rocket is launched, shooting 50.0 g of burned fuel from its exhaust at an
average velocity of 625 m/s. What is the velocity of the rocket after the fuel has burned?
(Ignore effects of gravity and air resistance.)