Question

A ball is projected upwards. The time corresponding to height h while ascending and descending are t₁ & t₂ respectively. What is the speed of projection ? take acceleration due to gravity as 10 m/s². 

(a) 10t₁

(b) 10t₂ 

(c) 10(t₁ + t₂) 

(d) 5(t₁ + t₂) 

Answer 1

Answer is (d) 5(t₁ + t₂)

here h = ut – (1/2) gT². that is (1/2) gt² – ut + h = 0 

this is an quadratic equation in t.

hence t₁ + t₂ = b/a = u/((1/2) g) = u/5. 

That is u = 5 (t₁ + t₂)