Question

A bullet is shot upwards with an initial velocity of 100 ft/sec from a point 5 ft above the ground, and its height above the ground at time t is given by h (t) = − 25 1² + 100 + 5

i. How high will the bullet go?
ii. How long will it take the bullet to reach the highest point?

Answer 1

To determine the maximum height of the bullet, we can find the vertex of the quadratic function representing the height of the bullet. Using the formula t = -b/(2a), where a = -25 and b = 100, we find that the highest point is reached after 2 seconds. Substituting this value back into the equation, the bullet will reach a maximum height of 105 feet.

Step-by-step explanation:

To determine how high the bullet will go, we need to find the maximum height of the bullet's trajectory. In this case, the equation for the height of the bullet is h(t) = -25t^2 + 100t + 5. To find the maximum height, we need to find the vertex of this quadratic function. The vertex is the highest point on the trajectory and can be found using the formula t = -b/(2a), where a = -25 and b = 100.

Substituting the values of a and b into the formula, we have t = -100/(2(-25)) = -100/(-50) = 2 seconds. So, the bullet will reach its highest point after 2 seconds.

To find the maximum height, we can substitute the value of t back into the equation: h(2) = -25(2)^2 + 100(2) + 5 = -100 + 200 + 5 = 105 feet. Therefore, the bullet will reach a maximum height of 105 feet.