Numerical Solution (Kinemetics)

[2075 S, 2069 S]

A swimmer's speed along the river (downstream) is $20 \; km/h$ and can swim up-stream at $8\; km/h$, Calculate the velocity of the stream and the swimmer's possible speed in still water.

2075 B

A body is projected upwards making an angle $'\theta'$ with the horizontal with a velocity of $300\;m/s$. Find the value of $'\theta'$ so that the horizontal range will be maximum. Hence find its range and time of flight.

2074 S

A stone on the edge of a vertical cliff is kicked so that its initial velocity is $9\;m/s$ horizontally. If the cliff is $200\;m$ high, calculate: (i) time taken by stone to reach the ground. (ii) How far from the cliff the stone will hit the ground?

2074 B / 2073 S / 2066

A projectile is fired from ground level with a velocity $500\;m/s$ at $30{\circ}$ to the horizontal. Find its horizontal range, the greatest height and the time to reach the greatest height.

2073 C

A batter hits a base ball so that it leaves the bat with an initial speed $37\; m/s$ at an angle $53^{\circ}$. Find the position of the ball and the magnitude and direction of its velocity after $2$ seconds. Treat the baseball as a projectile. [Click here for solution]

2072 S, 2069 B

A baseball is thrown towards a player with an initial velocity $20\;m/s$ and $45^{\circ}$ with the horizontal. At the moment, the ball is thrown the player is $50\;m$ from the thrower. At what speed and in what direction must he run to catch the ball at the same height at which it is released?

2072 D

An airplane is flying with a velocity of $90\;m/s$ at an angle of $23^{\circ}$ above the horizontal. When the plane is $114\;m$ directly above a dog that is standing on level ground, a suitcase drops out of luggage compartment. How far from the dog will the suitcase land? You can ignore air resistance.

2071 C

A bullet is fired with a velocity of $100\;m/s$ from the ground at an angle of $60^{\circ}$ with the horizontal. Calculate the horizontal range covered by the bullet. Also, calculate the maximum height attained.

[2070 S - A] 

A car travelling with a speed of $15\;m/s$ is braked and it slows down with uniform retardation. It covers a distance of $88 \; m$ as its velocity reduces to $7 \;m/s$. If the car continues to slow down with same rate, after what further distance will it be brought to rest? [Click here for solution]

2070 S - B

A stone is projected horizontally with $20\;m/s$ from the top of a tall building. Caklculate its position and velocity after $3\;Sec$ neglecting the air resistance.

2069 S

An object with mass $m$ moves along the x-axis. Its position as a function of time is given by $x(t) = At  - Bt^3$, where $A$ and $B$ are constants. Calculate the net force on the object as a function of time.