Tossing a Coin in a Moving Train

A person is sitting in a moving train and is facing the engine. He tosses up a coin which falls behind him. He concludes that the train is moving-A person is sitting in a moving train and is facing the engine. He tosses up a coin which falls behind him. He concludes...

Vertical Motion

A boy is standing on top of a tower of height 85m and throws a ball in the vertically upward direction with a certain speed. If 5.25 secs later he hears the ball hitting the ground, then the speed with which the boy threw the ball is ( take g=10m/s2, speed of sound in...

Relative Velocity of Canoe in River

A canoe has a velocity of 0.40m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50m/s east relative to the earth. Find the velocity(magnitude and direction ) of the canoe relative to the river. Discussion: We apply the relative velocity...

Position of a Particle

A particle of mass m is subject to a force $$ F(t)=me^{-bt}$$. The initial position and speed are zero. Find \(x(t)\). Solution: In the given problem $$ \ddot{x}=e^{-bt}$$ Integrating this with respect to time gives $$ v(t)=-\frac{e^{-bt}}{b}+A $$ ( A is the constant...

Instantaneous Velocity and Acceleration

Let \(\vec{v}\) and \(\vec{a}\) be instantaneous velocity and the acceleration respectively of a particle moving in a plane. The rate of change of speed (dv/dt) of the particle is: (a) \(|a|\) (b) \((v.a)/|v|\) (c) the component of \(\vec{a}\) in the direction...