Question

If an object is projected at a given angle and speed, how long does it take to reach its maximum height?

Please explain in simplest terms and give an example using units given.

Answer 1

If an object is projected at a given angle and speed, so the speed which is velocity in this case has vertical and horizontal components. Now if we consider the negligible air friction so the object doesn't have any positive and negative acceleration in horizontal direction but as the gravity pulls down the object, thus it has negative acceleration which opposes the vertical velocity of the object and take it is in the rest at a certain point which we express as the Maximum height.

Formula for the maximum height of projectile motion,

H = u*(Sin ß)/g

where H is the maximum height, u is speed of projection, ß is the angle of projection and g is acceleration due to gravity.

Example:-

a ball is projected at 30° with the speed of 25 m/s. find out the maximum height attained by the ball.(take g = 9.8 m/s²)

Solution: Velocity of projection,u = 25 m/s

Angle of projection, ß = 30°

Expression for the maximum height is,

H = u * (Sin ß)/g

H = 25 * (Sin 30°)/9.8

H = 1.28 m

The Maximum height attained by the ball is 1.28 m.