hello please help with this. i can't understand how to complete these questions
2. The height, H meters, of a falling object is related to the time, t seconds, the object has been falling by the formula h=-4.9t^2+d , where d meters is the initial height of the object above the ground. The bankers hall building is 196m tall. express the time an object takes to reach the ground from this height as an exact number of seconds.
5. The volume of a cone with height, h (m), and radius r (m), is given by the formula v=1/3πr^2h. What is the radius of a cone with volume 168cm^3 and height 9cm.
h=-4.9t^2+d
d = 196
when is h = 0?
4.9 t^2 = d
t^2 = d/4.9
t = sqrt (196/4.9) = sqrt(40) = 2 sqrt (10)
v= (1/3) π r^2 h. What is the radius of a cone with volume 168cm^3 and height 9cm.
v = 168 cm^3
h = 9 cm
168 * 3 = π r^2 (9)
59 = π r^2
r = sqrt(59/π) centimeters
Sure! I can help you with these questions.
Question 2:
To express the time that the object takes to reach the ground as an exact number of seconds, we need to set the height h to 0 because the ground is at a height of 0. Then we can solve for the time t.
The formula given is h = -4.9t^2 + d, where h is the height, t is the time, and d is the initial height above the ground. In this case, the initial height above the ground is 196 meters, so d = 196.
Setting h = 0, we have:
0 = -4.9t^2 + 196
To solve this equation for t, we can rearrange it to isolate t:
4.9t^2 = 196
t^2 = 196 / 4.9
t^2 = 40
t = √40
t ≈ 6.32
Therefore, the object takes approximately 6.32 seconds to reach the ground from a height of 196 meters.
Question 5:
To find the radius of a cone with a given volume and height, we can use the formula v = 1/3πr^2h, where v is the volume, r is the radius, and h is the height.
The formula given is v = 168 cm^3 and h = 9 cm. We need to solve for r.
1/3πr^2h = v
Plugging in the values, we have:
1/3πr^2 * 9 = 168
To solve this equation for r, we can first multiply both sides by 3 to get rid of the fraction:
πr^2 * 9 = 168 * 3
πr^2 * 9 = 504
Next, divide both sides by 9π to isolate r^2:
r^2 = 504 / 9π
r^2 ≈ 18.03
Finally, take the square root of both sides to solve for r:
r ≈ √18.03
r ≈ 4.25
Therefore, the radius of the cone with volume 168 cm^3 and height 9 cm is approximately 4.25 meters.