1. A projectile is fired and in 10 s it hits the ground with final velocity of 0

Question

1. A projectile is fired and in 10 s it hits the ground with final velocity of 0.5 km/s at an angle of 60° below the horizontal. Find displacement and initial velocity of the projectile as well as the maximum altitude of its trajectory.

2. Two blocks of mass 1 kg and 2 kg are connected by a massless rope passing over a 3 kg pulley of radius 10 cm. Find angular acceleration of the pulley if the coefficient of friction between the 2 kg block and the support is 0.2. Find also force of tension in the rope.

3. A pendulum bob of a mass 500 g oscillates on a 2 m long string. When the bob is 10° away from equilibrium, its kinetic energy is 0.1 J. Find amplitude of the pendulum. Find centripetal force and tension in the pendulum string when the bob is in the point of maximum deviation from equilibrium.

4. Find initial temperature of a 3 cm ice cube, which, when put into 500 ml of boiling water, reduces its temperature to 80°C.

3. A pendulum bob of a mass 500 g oscillates on a 2 m long string. When the bob is 10° away from equilibrium, its kinetic energy is 0.1 J. Find amplitude of the pendulum. Find centripetal force and tension in the pendulum string when the bob is in the point of maximum deviation from equilibrium.

4. Find initial temperature of a 3 cm ice cube, which, when put into 500 ml of boiling water, reduces its temperature to 80°C.

Explanation / Answer

1.

here by using the formula

t = 2 * v0 * sin(theta) / g

10 = 2 * v0 * sin(60deg) / 9.8

v0 = 10 * 9.8 / 2 * sin(60deg)

v0 = 56.58 m/s

the intial velocity is 56.58 m/s

then

the maximum height = v0^2 * sin(theta)^2 / 2 * g

H = 56.58 * sin(60deg)^2 / 2 * 9.8

H = 2.165 m

the maximum height is 2.165 m

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