Question

An object is in free fall. After 10 seconds calculate the distance fallen? *

A diver jumps off a 60 m cliff with an initial horizontal velocity of 3m/s. Find the time needed to reach water?

Answer 1

*For free fall,

Initial velocity (u) = 0

g = 9.8m/s²

time(t) = 10s

Using the second equation of free fall;

s = ut + 1/2gt²

where 's' is the distance fallen.

s = 0(10) + 1/2(9.8)(10)²

s = 1/2(9.8)(100)

s = 490m.

*Initial horizontal velocity (Ux) = 3m/s

Initial vertical velocity (Uy) = 0

since it did not start with any vertical velocity.

Using the second equation of vertical downward motion:

h = Uyt + 1/2gt²

where h is the height of the cliff = 60m.

g = 9.8m/s²

60 = 0(t) = 1/2 (9.8)(t²)

60 = 4.9t²

t = √(60/4.9) = 3.5s.

Answer 2

9.81 × 10 = 98.1 meters

vertical displacement is s=1/2 at^2 + vt

initial vertical velocity is 0 so s=1/2 at^2

a in this instance is gravitational acceleration so 60m= 1/2 (9.81)t^2

solve for t, t = 3.497s. //I corrected this answer as just now I misread horizontal as vertical.