Question

A cannonball is shot into the air on an alien planet. The path of the cannonball is modeled by the set of parametric equations x=59t, y=65t-2.1t^2 where t is time in seconds, and x and y are in meters. Assume the ground is at y=0. What is the maximum height attained by the cannonball?

a) 828.81 m
b) 414.40 m
c) 502.98 m
d) 489.69 m
e) 913.095 m

Answer 1

The maximum height attained by the cannonball is a. 828.81 meters.

Step-by-step explanation:

To find the maximum height attained by the cannonball, we can use the equation y = 65t - 2.1t^2. The maximum height occurs when the cannonball reaches its highest point, which happens when the vertical velocity is equal to zero.

To find the time when the vertical velocity is zero, we can set the derivative of y with respect to t equal to zero and solve for t.

Setting the derivative equal to zero, we get 65 - 4.2t = 0. Solving for t, we find t = 15.47619 seconds.

Substituting this time back into the equation y = 65t - 2.1t^2, we can find the maximum height. Plugging in t = 15.47619, we get y = 65(15.47619) - 2.1(15.47619)^2 = 828.81 meters.

Therefore, the maximum height attained by the cannonball is 828.81 meters.