Question

If the time of flight of a projectile is doubled, what happens to the maximum height attained?
a. Halved
b. Remains unchanged
c. Doubled
d. Becomes four times

Answer 1

Time of flight is the time taken by body to reach the projection. The vertical displacement during time of ascent is the maximum height. The energy stored as a result of deforming an elastic body is termed as Elastic potential. Use the above statement to find the relation between the time of flight and the maximum height obtained.

Complete step by step solution:
A body projected in air at an angle other than ninety degree is called projectile. Time of flight is the time taken by body to reach the projection. The vertical displacement during time of ascent is the maximum height. Free body diagrams will consist of a simplified version of the body. The energy stored as a result of deforming an elastic body is termed as Elastic potential. In common assumptions air resistance and friction are neglected.
The energy will be retained until the force is removed and the springs reach its original shape. Potential energy is the energy stored due to its location or configuration.

The energy possessed by a body due its motion is termed as Kinetic energy. It is determined that the body can do work against a restraining force action on the body before the body comes to rest.
Here maximum height is given by $H = \dfrac{{{u^2}{{\sin }^2}\theta }}{{2g}}$
Let’s multiple 4 to the numerator and denominator
$H = \dfrac{{4{u^2}{{\sin }^2}\theta }}{{8g}}$
Compare this time of flight equation then
$H = \dfrac{{{t^2}}}{8}$
Since $t = \dfrac{{2u\sin \theta }}{g}$
Thus, we know that $H$ is directly proportional to the square of the time of flight. If time of flight doubles then the maximum height will increase by 4 times.

Hence, the correct answer is option (D).

Note: Potential energy is the stored energy inside the body, when the body is deformed. When the body retains its original state, the potential energy stored in the body will get converted to kinetic energy. Potential energy is the energy stored due to its location or configuration. The energy possessed by a body due its motion is termed as Kinetic energy.