Final answer:
To find the time it takes for the apple to hit the ground, calculate the initial vertical velocity using the sine function and then apply the kinematic equation factoring in gravity's acceleration to find the total duration the apple remains in the air.
Step-by-step explanation:
To determine how long it takes for an apple tossed at an angle of 57 degrees above the horizontal at 9.5 m/s to hit the ground, we need to consider the vertical components of the motion, as horizontal motion does not affect the time it takes to fall.
The initial vertical velocity (vy) can be found by using the formula vy = v * sin(θ), where v is the initial velocity and θ is the angle of projection. For this case, vy = 9.5 m/s * sin(57°).
Using the kinematic equation for vertical motion with constant acceleration due to gravity (g = 9.8 m/s2), we can express the time (t) it takes to reach the maximum height and then fall back to the ground as t = 2*vy/g. This time accounts for the ascent and descent of the projectile.
Plugging in the values, we find the total time in the air, which would allow us to select the correct answer from the options provided.