# Math 10

Hello,
Is there easiest and simplest way to do this question?

"A baseball is thrown from the top of a building and falls to the ground below. The height of the baseball above the ground is approximated by the relation h = -5t2 + 10t + 15, where h is the height above the ground in metres and "t" is the elapsed time in seconds. Determine the maximum height that is reached by the ball."

Thank you very much!

1. 👍 0
2. 👎 0
3. 👁 274
1. that is a parabola (quadratic)

5 t^2 - 10 t - 15 = -h

find the vertex by completing the square

t^2 - 2 t - 7.5 = -(1/5)(h)

t^2 - 2 t = -h/5 + 7.5

t^2 - 2 t + 1 = -h/5 + 8.5

(t-1)^2 = -(1/5) (h - 42.5)

so max height at one second of 42.5 meters

1. 👍 0
2. 👎 0
2. sure, all you have to do is to find the vertex of this "downwards" parabola.

I will assume that you do not know Calculus , so
(easiest way):

the x of the vertex for y = ax^2 + bx + c
is -b/(2a)
t of the vertex is -10/-10 = 1
sub into the equation ....
h = -5(1^2) + 10(1) + 15
= -5 + 10 + 15 = 20
vertex is (1,20)

so the ball reaches a max of 20 m after 1 second

1. 👍 0
2. 👎 0
3. t^2 - 2 t - 3 = -(1/5)(h)

t^2 - 2 t = -h/5 + 3

t^2 - 2 t + 1 = -h/5 + 4

(t-1)^2 = -(1/5) (h - 20)

so max height at one second of 20 meters

1. 👍 0
2. 👎 0

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Ratios of Similar Figures

1. Write the following ratio in simplest form: 32 min : 36 min a. 8 : 9 b. 8 : 36 c. 32 :9 d. 128 : 144 2. In a sports equipment locker, there are 81 balls and 45 baseball mitts. Write the ratio of balls to baseball mitts in

2. ### physics

The fastest recorded pitch in Major League Baseball was thrown by Nolan Ryan in 1974. If this pitch were thrown horizontally, the ball would fall 0.809 m (2.65 ft) by the time it reached home plate, 18.3 m (60 ft) away. The

3. ### physics

need HELP!! which of the following exhibits parabolic motion a. stone thrown into a lake b. space shuttle orbiting Earth c. leaf falling from a tree d. train moving along a flat track which of the following does NOT exhibits

A baseball is thrown at an angle of 40.0° above the horizontal. The horizontal component of the baseball’s initial velocity is 12.0 meters per second. What is the magnitude of the ball’s initial velocity?

1. ### English

Which is __________ to write, a letter or an essay? A. most easiest B. more easy C. easiest D. easier

2. ### Math

Question: Is 38/53 in simplest form? Explain why or why not. If not, write it in simplest form. My Written Answer: 38/53 is in it's simplest form because the greatest and only common factor of 38 and 53 is one and if you divide 38

The height y (in feet) of a baseball thrown by a child is y = -1/10 x^2 + 3x + 6 where x is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to

4. ### Physics

The velocity of the baseball as it leaves the bat is 38.2 m/s. Determine (a) the maximum height the baseball reaches, and (b) the total timke the baseball is in the air. Assume the baseball is caught at the same height above the

1. ### math

A baseball is thrown up in the air from a height of 3 feet with an initial velocity of 23 feet per second. When does the baseball hit the ground?

2. ### Physics

The fastest recorded pitch in major-league baseball, thrown by Nolan Ryan in 1974, was clocked at 100.8 mi/h. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached

3. ### math

Multiple Choice 1. Write the following ratio in simplest form: 32 min : 36 min (1 point) 8 : 9 8 : 36 32 : 9 128 : 144 2. In a sports equipment locker, there are 81 balls and 45 baseball mitts. Write the ratio of balls to baseball

4. ### Math Help!!!

In a sports equipment locker, there are 81 balls and 45 baseball mitts. Write the ratio of balls to baseball mitts in simplest form. A. 9:5 B. 10:18 C. 10: 5 D. 9:18 Is the answer A?