A 75.0 kg student throws a 70.0 kg professor horizontally out of a 35.0 kg boat

Question

A 75.0 kg student throws a 70.0 kg professor horizontally out of a 35.0 kg boat on an isolated lake. If the student and the boa, together recoil with a speed of 2.00 m/s how fast was the professor thrown from the boat? A 900 kg car initially going 15 m/s only in the x-direction runs into a stationary 1500 kg truck. After the collision the car is going 5.0 m/s at an angle of 40 degrees above the x-axis. What is the magnitude and direction of the velocity if the truck right after the collision? A 14.9 g bullet is fired vertically into a 2.50 kg block suspended from the ceiling. The bullet imbeds in the block in an inelastic collision. If after the collision the block (with the bullet in it) swings up to a height of 37.9 cm, what was the velocity of the bullet? A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s^2. If the tires have a radius of 0.330 meters, how many revolutions does each tire make before the car comes to a stop? A small 0.400 kg mass swings on the end of a 2.00 m long light string. At the moment when the string makes an angle of 15 degrees with the vertical the mass has a speed of 6.20 m/s. Find (a) the tension in the string, (b) the centripetal acceleration, (c) the tangential acceleration and (c) the total acceleration. A bug hangs on by friction to a horizontal spinning disk at a radius of 34.1 cm. If the coefficient of friction between the bug and the disk is 0.870 at what angular velocity must the disk spin to cause the bug to slide off? How many revolutions per second?

Explanation / Answer

Let V be the speed of the block with the bullet inside just after the collision.

from law of conservation of energy

1/2 mV2 = mgh

V=(2gh)

V=(2*9.8*37.9*10-2) = 2.725 m/s

from conservation of momentum

mAvA = (mA+mB)V

14.9*10-3 kg *vA = (14.9*10-3 kg + 2.5 kg ) 2.725 m/s

vA = 459.93 m/s

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