# Calculus

posted by .

A ball is thrown straight down from the top of a 220-foot building with an initial velocity of -22 feet per second. What is its velocity after 3 seconds? What is its velocity after falling 108 feet?

• Calculus -

equation:
s = -16t^2 - 22t + 220
v = ds/dt = -32t - 22
so at t=3
v = -16(3) - 22 = -70 ft/sec

when s = 108
108 = -16t^2 - 22t + 220
16t^2 + 22t - 112 = 0
t = (-22 ± √7652)/32 = 2.046 sec or a negative time

so when t = 2.046
v = -16(2.046) - 22 = - 54 ft/s

• Calculus -

s = -16t^2 - 22t + 220
v = ds/dt = -32t - 22
so at t=3
v = -32(3) - 22 = -118 ft/sec

when s = 108
108 = -16t^2 - 22t + 220
16t^2 + 22t - 112 = 0
t = (-22 ± √7652)/32 = 2.046

so when t = 2.046
v = -32(2.046) - 22 = -87.472 ft/s

The process is correct but the t=2.046 should be substituted to the first derivative which is velocity function.

## 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 time …
2. ### 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 time …
3. ### algebra

5. 16t2 gives the distance in feet a free-falling object falls in t seconds. 16t2 + 10t gives the distance an object falls in t seconds when it is thrown down with an initial velocity of 10 feet per second. Use this polynomials to: …
4. ### calculus

If a ball is thrown straight up into the air with an initial velocity of 70 ft/s, it height in feet after t second is given by y = 70 t - 16 t^2. Find the average velocity for the time period begining when t = 1 and lasting (i) 0.1 …
5. ### Calculus

1. The problem statement, all variables and given/known data a ball is thrown straight down from the top of a 220 feet building with an initital velocity of -22ft/s. What is the velocity of the ball after 3 seconds?

1. The problem statement, all variables and given/known data a ball is thrown straight down from the top of a 220 feet building with an initital velocity of -22ft/s. What is the velocity of the ball after 3 seconds?
7. ### math

An object that is falling or vertically projected into the air has it height, in feet, above the ground given by the formula below, where s is the height in feet, Vo is the original velocity of the object, in feet per second, t is …
8. ### Math

A ball is thrown downward from the top of a 100-foot building with an initial velocity of 14 feet per second. The height of the ball h after t seconds is given by the equation h=-16t^2-14t+100. How long after the ball is thrown will …
9. ### calculus

A ball is thrown vertically upward with an initial velocity of 128 feet per second, the ball’s height after t second is s(t) = 128t – 16t². Find the instantaneous velocity at 4 seconds.
10. ### Calculus - Falling Body Problem

Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 3000 feet with a …

More Similar Questions