Question

A dart is thrown upward with an initial velocity of 18 ft/s at an angle of elevation of 59°. Consider the position of the dart at any time t. Neglect air resistance. (Assume t is in seconds. Round your answer to one decimal place.) At what time will the dart reach maximum height?

Answer 1

The dart will reach maximum height at approximately 0.6 seconds.

Step-by-step explanation:

The maximum height of a projectile can be found by analyzing its vertical motion. In this case, the dart is thrown upward with an initial velocity of 18 ft/s at an angle of elevation of 59°.

Since the projectile's initial vertical velocity is 18 ft/s * sin(59°), we can determine the time it takes for the dart to reach maximum height using the equation:

t = (vertical velocity) / (acceleration due to gravity)

Plugging in the values, we have:

t = (18 ft/s * sin(59°)) / (-32.2 ft/s²)

Simplifying the expression, we get:

t ≈ 0.58 s

Therefore, the dart will reach maximum height at approximately 0.6 seconds.