Final answer:
The speed of the ball 3 seconds after being projected horizontally from a cliff will be approximately 49.4 m/s when there is no air resistance.
Step-by-step explanation:
When a ball is projected horizontally with a speed of 40 m/s from the top of a cliff on the surface of the earth and there is no air resistance, the horizontal velocity remains constant since no horizontal forces are acting on the ball.
The only force acting on the ball is gravity, pulling it downward vertically.
Therefore, the vertical velocity will increase due to gravitational acceleration (approximately 9.81 m/s2).
After 3 seconds, the vertical velocity will be 9.81 m/s2 × 3 s = 29.43 m/s (downward).
To find the total speed of the ball 3 seconds later, we can use the Pythagorean theorem because the horizontal and vertical components of velocity are orthogonal.
The total speed V can be calculated as V = sqrt(Vx2 + Vy2), where Vx is the horizontal velocity and Vy is the vertical velocity.
Substituting the values, we get V = sqrt((40 m/s)2 + (29.43 m/s)2), which gives us the total speed of the ball 3s later as 49.4 m/s (approximately).