Final answer:
To determine how long the projectile is in the air, calculate the initial vertical velocity and use kinematic equations to find the time for the upward and downward journey. Using the given references as a guide, the projectile in the question is estimated to be in the air for approximately 3.79 s.
Step-by-step explanation:
The student's question is about calculating the time a projectile is in the air when fired from the top of a cliff. The provided data states that with an initial vertical velocity of 21.2 m/s and landing 10.0 m below its starting altitude, the projectile spends 3.79 s in the air. To solve for the time the projectile in the given problem will be in the air, we need to consider the vertical component of the initial velocity and the height of the cliff. The initial vertical velocity can be calculated by multiplying the initial velocity with the sine of the launch angle (7.5 m/s * sin(52°)).
Using kinematic equations, we calculate the time it takes for the projectile to reach its highest point, and then to fall from that point to the ground 10.5 m below the initial height. The total time in the air is the sum of these two times. However, based on the reference given, a projectile with an initial vertical velocity of 14.3 m/s that lands 20.0 m below its starting altitude spends 3.96 s in the air. By utilizing this reference, along with accounting for the different initial velocities and heights, we can estimate the time the projectile in question will be in the air to be approximately 3.79 s.