Question

Unimpressed with your previous stunt, the director of the new James Bond movie has come to you with a more exciting idea. In this stunt, Bond will run towards a bridge that is 26m above a river. His partner is in a speedboat 75 meters away from the bridge. Bond jumps horizontally off the bridge with a speed of 6.7 m/s toward where his partner is waiting. Starting from rest, his partner begins racing toward the bridge the moment Bond jumps. What is the minimum acceleration his partner will need in order to catch Bond before he hits the water?

Answer 1

This problem is based on projectile motion and kinematics,

As bond jumps horizontally, there is no vertical component of velocity.

We can find the time in air for Bond.

h_f = h_i + v_yt + 1/2a_yt²

0 = 26 + 0 - 1/2 * 9.8 * t²

t = 2.3035 seconds

distance covered by bond, d = vt

d = 6.7 * 2.3035

d = 15.433 m

Therefore, Bond's partner has only 2.3035 seconds and have a distance of 75 - 15.433 = 59.56 m to catch him.

Using kinematics, we have

d = ut + 1/2at²

as his partner starts from rest, u = 0

so,

d = 1/2at²

a = 2d / t²

a = 2 * 59.56 / 2.3035²

a = 22.45 m/s²