Final answer:
To calculate the maximum height attained by an arrow launched from a platform, apply the equations of motion for projectile motion using the given initial velocity, acceleration due to gravity, and platform height. The time to reach the peak is derived first, followed by the vertical displacement at the peak, which is then added to the initial platform height to find the maximum height.
Step-by-step explanation:
To find the maximum height attained by an arrow launched upward from a platform, we need to apply the formulas of projectile motion. Since the question states that the arrow is launched with an initial velocity of 256 feet per second from a 100-foot platform, we can calculate the maximum height using the following equations of motion under constant acceleration:
- First, we find the time of flight (t) to reach the peak by setting the final vertical velocity to zero (because at the peak, the velocity will be zero for an instant before the arrow begins to fall down) and using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (-32 feet per second squared, since it is directed downwards), and t is time.
- Once we find the time to reach the peak, we can calculate the displacement (y) of the arrow at the peak using the formula y = ut + 0.5 at².
- Finally, the maximum height is obtained by adding the initial platform height of 100 feet to the displacement y.
For the given problem,
- The initial vertical velocity u is 256 feet per second.
- The acceleration a is -32 feet per second squared.
- The initial platform height is 100 feet.
By solving these equations, we can find the time to reach the maximum height and then use that time to calculate the maximum height the arrow attains during its flight.