Question

1. A zebra sees a lion 300 m to his right. The zebra starts running at 25 KpH straight ahead to get away. At this point the lion launches himself on an intercept course at the zebra at a speed of 31 KpH.

At what angle does the lion launch himself?

If both animals continue to travel straight, how long does it take the lion to catch the zebra?

Answer 1

Speed of Zebra = 25 Kph = 6.94 m/s
Speed of Lion = 31 Kph = 8.61 m/s

Let us assume they meet at a point x meter ahead of Zebra Starting Point.

So Now,
Distance travelled by Zebra = x meter
Distance travelled by Lion = sqrt(x^2 + 300^2) meter

Time taken is same, Therefore

x/ 6.94 = sqrt(x^2 + 300^2) / 8.61
Solving for x
x = 408.6 m

Launch angle for Lion θ = tan^-1(408.6/300)
θ = 53.7^o

Time taken by Lion to Catch Zebra, t = 408.6 / 6.94 = 58.87 s
t = 59 s