Question

A ball when thrown vertically upwards with a velocity u reaches height h. If velocity is increased 2 times (i. e. 2 u) then what would be the effect on height?

Answer 1

The velocity of the ball will be zero at the highest point, therefore applying the formula.
v² = u² + as, we have
0 = u² – 2gh
or 2gh = u²
or h = \(\frac{u^{2}}{2 g}\)
When the initial velocity is doubled (i.e., 2v), then suppose the height becomes h’, therefore,
h’ = \(\frac{(2 u)^{2}}{2 g}=\frac{4 u^{2}}{2 g}=4 \times \frac{u^{2}}{2 g}\)
or h’ = 4h
Hence, on doubling the initial velocity, the height will become four times.