Answer :
Final answer:
To calculate the velocity of the plane, we use the equation of motion for vertical motion, h = ut + ½gt². Substituting the given values, we find that the velocity of the plane is approximately 189.05 m/s.
Explanation:
This problem is a classical physics problem and can be solved using equations of motion. We can ignore horizontal motion because it doesn't affect the time in which the projectile hits the ground. The only force acting vertically is gravity. Given the height (3000m) and the time (77 seconds) we can use the equation of motion to find the velocity of the plane - which is also the initial speed of the projectile.
The vertical motion is represented by the equation of motion: h = ut + ½gt² where h is the height, u is the initial velocity, t is the time and g is acceleration due to gravity. We know h (3000m), t (77s) and g (9.81m/s² - approximate value). We can rearrange the formula to u = h/t - ½gt. Substituting, we get: u = (3000 / 77) - 0.5*9.81*77 = -189.05 m/s. The negative sign indicates the direction of the velocity, opposite to the direction of g. However, we only care about the magnitude: so, the velocity of the plane is 189.05 m/s.
