# Calculus 1

A ball is thrown vertically upward from ground level with initial velocity of 96 feet per second. Assume the acceleration of the ball is a(t) = -32 ft^2 per second. (Neglect air Resistance.)

(a) How long will it take the ball to raise to its maximum height? What is the maximum heights?

(b) After how many seconds is the velocity of the ball one-half the initial velocity?

(c) What is the height of the ball when its velocity is one-half the initial velocity?

1. 👍
2. 👎
3. 👁
1. (a) Acceleration is Change in velocity over time, thus we can write it as,
a = (vf - vo) / t
Note that final velocity (vf) is Zero when it reaches its Maximum height since it stops. And since acceleration and Initial velocity (vo) are given, we can Substitute:
-32 = (0 - 96) / t
-32t = -96
t = 3 seconds

For Maximum height, we can use the formula,
h = vo*t - (1/2)(a)(t^2)
h = 96*3 - (1/2)(-32)(3^2)
h = 144 ft

1. 👍
2. 👎
2. (c) We can calculate for the height of the ball when it is 1/2 of Initial velocity using the formula,
vf^2 - vo^2 = 2gd
Since vf= 1/2*vo,
(1/2*vo)^2 - vo^2 = 2gd
Substituting,
(1/2*96)^2 - 96^2 = 2*(-32)*d
48^2 - 96^2 = -64d
d = -6912/-64
d = 108 ft

(b) We can calculate the time when the ball is moving at 1/2 of its Initial velocity with the same formula we used in (a),
h = vo*t - (1/2)(a)(t^2)
Substitute h = 108, and solve for t.

1. 👍
2. 👎

## Similar Questions

1. ### Algebra

THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the ground h(t) of an object thrown vertically from a height of h0 feet, with an initial velocity of v0 feet per second, if there is no air friction and t is the

2. ### Math-

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 a.) at what time will the ball strike the ground b.) for

3. ### Calculus

A ball is thrown straight up from the top of a hill 30 feet high with an initial velocity of 72ft/sec. How high above level ground will the ball get? (Objects subjected to gravity adhere to s(t) = -16t^2 + v0t + so where s is the

4. ### pre-calc

Physics: a ball is thrown vertically upward with an initial velocity of 80 feet per second. the distance (in feet) of the ball from the ground after t seconds if s=80t-16tt^2 a) draw the illustration b) for what time interval is

1. ### Physics

A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m. How high does the ball rise? How long does it take to reach its highest point? How long does the ball take to hit the ground after it reaches its

2. ### Calculus

Use a(t)=-32 ft/second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 96 feet per second. How high will it go?

3. ### algebra 2

A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. After t seconds, the height of the ball above the ground is s(t) = 16t2+ 96t + 200. a. After how many seconds

4. ### Pre-Calculus

A ball is thrown vertically upward with an initial velocity of 64 feet per second. The distance(in feet) of the ball from the ground after t seconds is s=64t-16t. At what time will the ball strike the ground? For what time t is

1. ### calculus

if a ball is thrown vertically upward with an initial velocity of 48 ft/s, then its height, s, after t seconds is given by s(t)= 48t-16t^2. a) what is the velocity of the ball after 1 second? b) when does the ball hit the ground?

2. ### Algebra

A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s=-16t^2+208t. After how many seconds will the ball be 640 feet from the ground?

3. ### Quadratic equations

A ball is thrown vertically upwards From the top of a building of height 29.4 m and with an initial velocity 24.5 m/sec. If the height H of the ball from the ground level is given by H = 29.4 + 24.5t - 4.9t², then find the time

4. ### Physics

Two students are on a balcony a distance h above the S street. One student throws a ball vertically downward at a speed vi ; at the same time, the other student throws a ball vertically upward at the same speed. Answer the