Question

An object is thrown vertically from a height how does the time of flight and the range of the object change when the magnitude of initial velocity tripled?

Answer 1

Time of flight is the amount of time taken by the projectile to complete its path. It is measured in seconds or we can say that it has a dimension of time. Time of flight depends on initial velocity of the projectile and not on the final velocity of the projectile. Time of flight is a very important factor for any projectile motion.

Complete answer:
The time of flight for a projectile can be given by
$T=\dfrac{2u\sin \theta }{g}$
Where “u” is the initial velocity of the object and “g” is the acceleration due to gravity.
$T\propto u$
As we can see in the formula that the time of flight is directly proportional to the initial velocity. So if the value of initial velocity is tripled the time of flight will increase by 3 times.
The range for the projectile can be given as
$R=\dfrac{{{u}^{2}}\sin 2\theta }{g}$
As we can see in the formula that the range of the projectile is directly proportional to the square of the initial velocity
$R\propto {{u}^{2}}$
Hence, we can say that the range of flight will be increased by 9 times if the value of initial velocity “u” is tripled.
Therefore, we can conclude that the time of flight will be increased by three times and the range of flight will be increased by 9 times if the initial velocity is tripled.

Note:
The range of flight is the maximum horizontal distance a projectile will cover. It is measured in meters or we can say that it has a dimension of length. Range of flight does not depend on the final velocity of the projectile as in the end the projectile has to complete its projection which may lead to zero final velocity.