Question

Alice and Bob are doing a space race from Earth to the Moon which is d~ 384000km far away. Alice's spaceship flies with a constant speed of v =500km/h. Bob's spaceship starts slowly but accelerates constantly with a=1.4km/h. Who win the race

Answer 1

distance between Earth to the moon , d = 384000 km

constant speed of Alice's spaceship , v = 500 km/h

so, time taken by Alice's spaceship to reach on the moon , t = 384000/500 = 3840/5 = 768 hours

constant acceleration of Bob's spaceship , a = 1.4 km/h²

Let T is the time taken by Bob's spaceship to reach on the moon.

using formula, S = ut + 1/2 at²

S = d = 384000 km , u = 0, a = 1.4 km/h²

so, 384000 = 1/2 × 1.4 × T²

or, 768000 = 1.4 × T²

or, T² = 768000/1.4 = 548571 h²

or, T = 740.655 hours

hence, it is clear that Bob win the race.