# calculus 2

A tomato is thrown upward from a bridge 23 m above the ground at 40 m/sec. Take the acceleration of gravity be equal to 9.8 m/s^2

(a) Give formulas for the acceleration, velocity, and height of the tomato at time t.

(b) How high does the tomato go, and when does it reach its highest point?

(c) How long is it in the air?

1. 👍
2. 👎
3. 👁
1. my equation would be

h = -4.9t^2 + 40t + 23
v = - 9.8t + 40
a = -9.8

b) max h, when v = 0
-9.8t+40=0
t = 40/9 seconds
h= -4.9(40/9)^2 + 40(40/9) + 23 = 103.99 m

c) let's find when it hits the ground, that is, when h = 0
-4.9t^2 + 40t + 23 = 0
4.9t^2 - 40t - 23 = 0
t = (40 ± √2050.8)/9.8
= 8.7 or some negative, which would be silly

It is in the air for appr 8.7 seconds

BTW, that is some feat to throw a tomato about 80 m up into the air !

1. 👍
2. 👎

## Similar Questions

1. ### math

A body is thrown vertically upward from the ground with an initial velocity of 96 ft/sec. Find the maximum height attain by the body

2. ### physics

A stone is thrown from the top of a building upward at an angle of 30.0∘to the horizontal and with an initial speed of 20.0 m/s. If the height of the building is 45.0 m, what is the speed in m/sec of the stone just before it

3. ### science

The acceleration of gravity on the surface of Venus is 8.9m/s^2. Would a ball thrown upward on Venus return to the ground sooner or later than a ball thrown upward with the same speed on the earth?

4. ### Math

For this problem, a person standing on the edge of a cliff throws a rock directly upward. it is observed that 2 secs later the rock is at its maximum height (in feet) and that 5 secs after that (meaning 7 seconds after being

1. ### Physics

A ball is thrown upward with an initial velocity of 14 m/s. Using the approximate value of g = 10 m/s2, how high above the ground is the ball at the following times? (a) 0.90 s after it is thrown (b) 2.10 s after it is thrown

2. ### Physics

A rock is thrown directly upward from the edge of the roof of a building that is 40.2 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Neglect any

3. ### Chemistry

The tomato is dropped. What is the velocity, v, of the tomato when it hits the ground? Assume 94.7% of the work done in Part A is transferred to kinetic energy, E, by the time the tomato hits the ground.

4. ### math

A ball is thrown from the edge of a cliff with an initial velocity of 60·m/s upward. Answer the following questions using + (upward) and - (downward) to indicate the direction of the velocity. Ignore air resistance and assume the

1. ### General Chemistry 1 college class

The tomato is dropped. What is the velocity, , of the tomato when it hits the ground? Assume 82.7 of the work done in Part A is transferred to kinetic energy, , by the time the tomato hits the ground. Express your answer

2. ### General Chemistry I

The tomato is dropped. What is the velocity, , of the tomato when it hits the ground? Assume 82.7 of the work done in Part A is transferred to kinetic energy, , by the time the tomato hits the ground. Express your answer

3. ### math

a ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity 80 m/ sec .the distance s of the ball from the ground after t seconds is s= 96+80t-4.9 t^2.after how many seconds does the ball

4. ### physical science

the acceleration of gravity on the surface of venus is 8.9 m/s2. would a ball thrown upward from venus return to the ground sooner or later than a ball thrown upward with the same speed on the earth?