Telangana Board Solutions for Chapter: Motion in a Plane, Exercise 1: EXERCISES

A projectile is fired at an angle of $60°$ to the horizontal with an initial velocity of $800 \mathrm{m}/\mathrm{s},$ find the time of flight of the projectile before it hits the ground.

For a particle projected slantwise from the ground, the magnitude of its position vector with respect to the point of projection, when it is at the highest point of the path is found to be $\sqrt{2}$ times the maximum height reached by it. Show that the angle of projection is ${\tan }^{-1} \left(2\right).$

An object is launched from a cliff $20 \mathrm{m}$ above the ground at an angle of $30°$ above the horizontal with an initial speed of $30 \mathrm{m}/\mathrm{s}.$ How far horizontally does the object travel before landing on the ground?

O is a point on the ground chosen as origin, A body first suffers a displacement of $10\sqrt{2} \mathrm{m}$ North-East, next $10 \mathrm{m}$ North and finally North-West. How far it is from the origin?

From a point on the ground a particle is projected with initial velocity $u,$ such that its horizontal range is maximum. Find the magnitude of average velocity during its ascent.

A particle is projected from the ground with some initial velocity making an angle of $45°$ with the horizontal. It reaches a height of $7.5 \mathrm{m}$ above the ground while it travels a horizontal distance of $10 \mathrm{m}$ from the point of projection. Find the initial speed of projection.

Wind is blowing from the south at $5 \mathrm{m}/\mathrm{s}.$ To a cyclist it appears to be blowing from the east at $5 \mathrm{m}/\mathrm{s}.$ Show that the velocity of the cyclist is $5\sqrt{2} \mathrm{m}/\mathrm{s}$ towards north - east.

A person walking at $4 \mathrm{m}/\mathrm{s}$ finds rain drops falling slantwise in to his face with a speed of $4 \mathrm{m}/\mathrm{s}$ at an angle of $30°$ with the vertical. Show that the actual speed of the rain drops is $4 \mathrm{m}/\mathrm{s}.$