You are traveling in a convertible with the top down. The car is moving at a constant velocity of 16.6 m/s, due east along flat ground. You throw a tomato straight upward at a speed of 9.85 m/s. How far has the car moved when you get a chance to catch the tomato?
hf=hi+1/2 g t^2 + vit
hf, hi=0
t= 2vi/g= solve that.
horizonal distance= t*16.6m/s
To determine the distance the car has moved when you catch the tomato, we need to calculate the time it takes for the tomato to reach its highest point and come back down to your hand. Then, we can multiply that time by the velocity of the car.
First, let's find the time it takes for the tomato to reach its highest point. We'll assume the motion of the tomato is in the vertical direction only. We can use the kinematic equation:
vf = vi + at
Where:
vf = final velocity (at the highest point, the velocity is 0 m/s)
vi = initial velocity (9.85 m/s upward, relative to the car)
a = acceleration (due to gravity, -9.8 m/s^2)
t = time (unknown)
Rearranging the equation, we have:
t = (vf - vi) / a
Substituting the values we have, we get:
t = (0 - 9.85) / (-9.8)
t = 1 second (rounded to the nearest second)
Now, since the car is moving at a constant velocity of 16.6 m/s due east, the distance it travels can be calculated using:
distance = velocity * time
Substituting the values:
distance = 16.6 m/s * 1 s
distance = 16.6 meters
Therefore, the car has moved approximately 16.6 meters when you get a chance to catch the tomato.