Question

Two particles are projected with the same speed in different direction in the same vertical plane. Both particles have same range. If their time of flights are 10 seconds and 25 seconds, then range is $(g=10m{s}^{-2})$

Answer 1

We know that the range $R=u^{2}Sin2\theta /g$ is same for angles $\theta$ and $90-\theta$ provided projection speed is same.

Suppose projection speed is $u$ then

time of flight from $T=2uSin\theta /g$ is obtained as $T_1=2uSin\theta /g$ and $T_2=2uSin(90-\theta )/g=2uCos\theta /g$

On dividing we get $T_1/T_2=10/25=0.4=tan\theta$ so $\theta =ta{n}^{-1}0.4={21.8}^0$ putting this value in expression for $T_1$ we get $u=134.77m/s$

So range will be $R=u^{2}Sin2\theta /g={134.77}^2\times 0.6896/10=1252meter$