Projectile Motion

A particle falling vertically from a height hits a plane surface inclined to horizontal at an angle with speed $v_0$ and rebounds elastically as shown in the figure. Find the distance along the plane where it will hit the second time.

A gun can fire shells with maximum speed $v_0$ and the maximum horizontal range that can be achieved is $R=\frac{v_0^2}{g}$.If a target farther away by distance $\Delta x$ (beyond $R$ ) has to be hit with the same gun as shown in the figure here. Show that it could be achieved by raising the gun to a height at least $\mathrm{h}=\Delta x\left[1+\frac{\Delta x}{R}\right]$.

A hill is $500 \mathrm{m}$ high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of $125 \mathrm{m} {\mathrm{s}}^{-1}$ over the hill. The canon is located at a distance of $800 \mathrm{m}$ from the foot of the hill and can be moved on the ground at a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A fighter plane is flying horizontally at an altitude of $1.5 \mathrm{km}$ with speed $720 \mathrm{km} {\mathrm{h}}^{-1}$. At What angle of sight (w.r.t horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target?

In dealing with the motion of a projectile in the air, we ignore the effect of air resistance on the motion. This gives trajectory as a parabola as you have studied. What would the trajectory look like if air resistance is included? sketch such a trajectory and explain why you have drawn it that way.

A boy throws a ball in the air at $60°$to the horizontal along a road with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1 }(36 \mathrm{km} {\mathrm{h}}^{-1})$. Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if the car has a speed of $18 \mathrm{km} {\mathrm{h}}^{-1}$. Give an explanation to support your diagram.

A boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give an explanation to support your diagram.

A ball is thrown from a rooftop at an angle of $45°$ above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have greatest acceleration? Explain.

A ball is thrown from a rooftop at an angle of $45°$ above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have smallest speed?

A ball is thrown from a rooftop at an angle of $45°$ above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have greatest speed?

A particle is projected in the air at some angle to the horizontal, moves along the parabola as shown in the figure, where $x$ and $y$ indicate horizontal and vertical directions respectively. Show in the diagram, direction of velocity and acceleration at points $A,B$ and $C$.

A particle slides down a frictionless parabolic $\left(y=x^2\right)$ track $\left(A-B-C\right)$ starting from rest at point $A$ as in figure. Point $B$ is at the vertex of parabola and point $C$ is at a height less than that of point $A$. After $C$, the particle moves freely in air as a projectile. If the particle reaches highest point at $P$, then

.

Two particles are projected in air with speed $v_0$ at angles ${\theta }_1$ and ${\theta }_2$, (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than of the second, then tick the right choices

In a two dimensional motion, instantaneous speed $v_0$ is positive, constant. Then which of the following are necessarily true?

The horizontal range of a projectile fired at an angle of $15°$ is $50\mathrm{m}$. If it is fired with the same at an angle of $45°$. Its range will be: