Answer to Question #245974 in Mechanics | Relativity for Taylor

Question

A cheetah can run at a maximum speed 105 km/h and a gazelle can run at a maximum speed of 76 km/h. If both animals are running at full speed, with the gazelle 79.2 m ahead, how long before the cheetah catches its prey? Answer in units of s.

Answer 1

$x = x_0+v_xt$

$\text{For cheetah: }\newline x_0 = 0;v_c= 105\frac{km}{h}$

$x= 105t(1)$

$\text{For gazelle: }\newline x_0 = 79.2m =79.2*10^{-3}km;v_c= 76\frac{km}{h}\newline x= 79.2*10^{-3}+ 76t(2)$

$\text{Equate (1) and (2):}\newline 79.2*10^{-3}+76t= 105t$

$t = \frac{79.2*10^{-3}}{29}h=\frac{79.2*10^{-3}*3600}{29}s=9.83s$

$\text{Answer: }9.83s$