Exercise 1

Show that there are two times for which the projectile covers the same vertical distance and their sum is equal to the time of flight.

A cricket ball is thrown with kinetic energy ${\mathrm{E}}_{\mathrm{k}}$ at an angle $45°$with the horizontal. Its kinetic energy at the highest point will be

A particle completes $5 rev/sec$ in a circle of radius $6 cm$. Calculate the linear velocity and centripetal acceleration and also find out the centripetal force where $m=0.2 kg.$

In figure, as the van moves at constant speed from point A to point B, the weight of a passenger recorded by a platform scale changes from $600 \mathrm{N}$ to $400 \mathrm{N}$. The speed of the van is close to

An aeroplane is flying at a height of $3000 m$ above ground level. If the angle subtended at the ground observation point by the aeroplane position $12 s$ apart is $30°$, what is the speed of the aeroplane?

A particle is projected with a certain velocity so as to pass through a point at a horizontal distance $R$ from the point of projection. Show that if $t_1$ and $t_2$ are the time taken to reach this point in two possible ways in which the particle can be projected with the given velocity then $t_1{t}_2=\frac{R}{g}$.

A projectile is fired on the Moon and on the earth with the same initial velocity and the same angle of projection. Neglecting air resistance, which projectile has greater range? Which reaches the maximum height first?

In a long jump, does the range of jumps depend on how high an athlete jumps?