the function is h(t)= -4.9t^2+2t+45 (t represents time in seconds and h represents height in metres.)
a) how tall is the building?
b) how long does it take the balloon to fall on the sidewalk?
c)determine the max height of balloon
What building?
And where does the balloon come in ?
The question states that the water balloon is thrown from the roof of a building. the path that the balloon follows the following function, which was listed above
Ok,
a) so when the balloon was thrown from the building
t = 0
so h = 0 + 0 + 45
The building is 45 metres high
b) when it hits the ground, h = 0
0 = -4.9t^2 + 2t + 45
4.9t^2 - 2t - 45 = 0
by the formula:
t = (2 ± √(4 - 4(4.9)(-45))/9.8
= 3.24 or a negative, which we would reject
it took 3.24 seconds to hit the ground
c) If you know Calculus ....
dh/dt = -9.8t + 2 = 0 for a max height
9.8t = 2
t = .2041 seconds
at that time, h = -4.9(.2041^2) + 2(.2041) + 45
= 45.2041m
If you don't know Calculus, then you probably learned how to complete the square
h = -4.9(t^2 -(2/4.9)t +.04165 - .04165) + 45
= -4.9(t - .2041)^2 + 45.2041
So the vertex is (.2041 , 45.2041) ---> max is 45.2041
(same as above)
To find the answers to these questions, we can analyze the given function.
a) To determine the height of the building, we need to find the value of h(t) when t represents the time it takes for the object to hit the ground, which is when h(t) equals 0. In other words, we need to solve the equation -4.9t^2 + 2t + 45 = 0. This is a quadratic equation, and we can solve it using various methods such as factoring, completing the square, or the quadratic formula. Once we find the value of t, we can substitute it back into the function h(t) to find the height.
b) To find how long it takes for the balloon to fall on the sidewalk, we need to determine the time when the height is zero. This is the same as solving the equation -4.9t^2 + 2t + 45 = 0. The value of t obtained from this equation would represent the time it takes for the balloon to fall.
c) To determine the maximum height of the balloon, we can analyze the equation. The coefficient of the t^2 term is -4.9, which is negative. This indicates that the graph of the function is a downward-opening parabola. The vertex of this parabola represents the maximum point. The t-coordinate of the vertex can be found using the formula t = -b/2a, where a is the coefficient of the t^2 term and b is the coefficient of the t term in the equation. Once we find the t-coordinate, we can substitute it back into the function h(t) to find the maximum height of the balloon.