The height(h) of an object that has been dropped or thrown in the air is given by: h(t)=-4.9t^2+vt+h

t=time in seconds(s)
v=initial velocity in meters per second (m/s)
h=initial height in meters(m)

A ball is thrown vertically upwardd from the top of the Leaning Tower of Pisa (height=53m) with an initial velocity of 30m/s. Find the time(s) at which:
a) the ball's height equals the hight of the tower
b) the ball's height is greater than the height of the tower
c) the ball's height is less than the height of the tower
d)the ball reaches its maximum height

I don't know how to do this problem.

Please Help and Thank You very much =)

heck, they gave you the equation.

h(t) = -4.9t^2 + 30t + 53

a) ball goes up, comes back down to the top of the tower. So, we want

53 = -4.9t^2 + 30t + 53
0 = -4.9t^2 + 30t
0 = t(-4.9t + 30)
so, t=0 (at the start) or t = 6.12 (as it comes back down)

b) same calculation but, t is between 0 and 6.12. That is 0 < t < 6.12

c) same calculation, but restricting t to positive values, t>6.12
Naturally, we could also restrict t to the point where height >= 0.

d) vertex of any parabola is where x = -b/2a = -30/-9.8 = 3.06

h(3.06) = 98.9

I don't get how you got:

vertex of any parabola is where x = -b/2a = -30/-9.8 = 3.06

h(3.06) = 98.9

where did all the numbers come from?

how did you get t=6.12 for a)???

To solve this problem, we need to use the given equation for the height of the object and substitute the values for the initial velocity and initial height.

a) To find the time(s) when the ball's height equals the height of the tower, we set h(t) equal to the height of the tower and solve for t:
-4.9t^2 + vt + h = 0

Substituting the values:
-4.9t^2 + 30t + 53 = 0

Next, we can solve this quadratic equation to find the value(s) of t.

b) To find the time(s) when the ball's height is greater than the height of the tower, we need to find all values of t where the height of the ball is greater than 53m. We can set up an inequality:
-4.9t^2 + 30t + 53 > 53

Simplifying, we get:
-4.9t^2 + 30t > 0

We can solve this inequality to find the range of values of t where the height is greater than 53m.

c) To find the time(s) when the ball's height is less than the height of the tower, we set up a similar inequality:
-4.9t^2 + 30t + 53 < 53

Simplifying, we get:
-4.9t^2 + 30t < 0

We can solve this inequality to find the range of values of t where the height is less than 53m.

d) To find the time when the ball reaches its maximum height, we need to find the vertex of the parabolic function -4.9t^2 + 30t + 53. The time value corresponding to the maximum height can be found using the formula for the x-coordinate of the vertex, -b/2a.

In this case, a = -4.9 and b = 30. We can plug in these values into the formula to find the time when the ball reaches its maximum height.

By following these steps, you should be able to solve all parts of the problem.