You are traveling in a convertible with the top down. The car is moving at a constant velocity 22.7 m/s, due east along flat ground. You throw a tomato straight upward at a speed of 14.9 m/s. How far has the car moved when you get a chance to catch the tomato?
To answer this question, we need to consider the horizontal and vertical motion separately. Let's start by calculating the time it takes for the tomato to reach its highest point.
The vertical motion of the tomato follows a projectile motion, where the only force acting on it is gravity. The initial vertical velocity is 14.9 m/s (upwards), and the acceleration due to gravity is 9.8 m/s^2 (downwards). We can use the formula Vf = Vi + at to find the time it takes to reach the highest point.
Vf = 0 m/s (at the highest point)
Vi = 14.9 m/s
a = -9.8 m/s^2
0 = 14.9 - 9.8t
Solving for t, we find t = 1.52 s.
Now, let's consider the horizontal motion. The car is moving at a constant velocity of 22.7 m/s due east. This means that while the tomato is in the air, it will continue to move horizontally with the same velocity as the car.
The horizontal distance covered by the car can be calculated by multiplying the car's velocity by the time it takes for the tomato to reach its highest point:
Distance = Velocity x Time
= 22.7 m/s x 1.52 s
Calculating the distance, we find that the car has moved approximately 34.56 meters when you get a chance to catch the tomato.