Question

The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.

An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?

a)0 = –4.9t2 + 19.6t + 24.5
b)0 = –4.9t2 + 24.5t + 19.6
c)19.6 = –4.9t2 + 24.5t
d)24.5 = –4.9t2 + 19.6t

Answer 1

s(t) = -4.9t² + 39.2t

Explanation:

Given the projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s²

Given

g = -4.9m/s²

v0 = 39.2m/s

s0 = 0m (the initial height)

On substituting into the formula;

s(t) = gt² + v0t + s0

s(t) = -4.9t² + 39.2t + 0

s(t) = -4.9t² + 39.2t

This gives the equation that models the height