A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t)=96t-16t^2
projectile formula: s(t)=1/2gt^2+v+t+h
g=acceleration due to gravity. V= the initial velocity, h= initial height, t=time, and s(t)= height at given time t
d. Explain how the equation relates to gravity and the projectile formula?
You made a typo. Assuming that gravity pulls downward, it should be
s(t)= -1/2 gt^2 + vt + h
(d) is poorly worded. The equation relates the motion to acceleration by gravity. It combines the initial conditions (v and h) with the influence of gravity.
The equation s(t) = 96t - 16t^2 describes the distance of a ball from the ground after t seconds when it is thrown vertically upward with an initial velocity of 96 feet per second.
The equation s(t) = 1/2gt^2 + v*t + h, known as the projectile formula, represents the trajectory of a projectile. In this formula, g represents the acceleration due to gravity, v represents the initial velocity, h represents the initial height, t represents time, and s(t) represents the height at a given time t.
Comparing the two equations, we can see that s(t) = 96t - 16t^2 matches the projectile formula. It aligns with the projectile formula because the initial velocity v is 96 feet per second, the height h is not given (assumed to be zero as it is thrown from the ground), and the term -16t^2 represents the effect of gravity, as it is proportional to the acceleration due to gravity (g).