I riding in a car at constant velocity and see an open manhole. I take out an watermelon and hold it out window. My speed is 10m/s and the initial height of watermelon is 1 m. I need to do a calculation to be able to know how far ahead of manhole I have to drop watermelon so it goes into the hole. I need to show calculations and resulting lead distance for successfully getting the fruit into the hole.-
Where do I start?
To determine the distance that you need to drop the watermelon ahead of the manhole, you'll need to consider the horizontal motion of the car and the vertical motion of the watermelon. Let's break it down into steps:
Step 1: Analyze the horizontal motion of the car
Since the car is moving at a constant velocity, its horizontal motion remains unaffected. This means that the car will maintain its velocity of 10 m/s and cover equal distances in equal intervals of time.
Step 2: Analyze the vertical motion of the watermelon
The watermelon is initially held at a height of 1 meter from the ground. When you drop it, it will fall vertically downwards under the influence of gravity. The vertical motion can be characterized using the equations of motion.
In this case, we only need to consider the vertical displacement (height) of the watermelon, as we want to drop it directly into the manhole. We also know that the acceleration due to gravity, represented by "g," is approximately 9.8 m/s².
The equation for displacement in vertical motion is given by:
h = vit + (1/2)gt²
In our case, the initial velocity (vi) of the watermelon is 0 since it starts from rest when you drop it. Therefore, the equation simplifies to:
h = (1/2)gt²
Step 3: Determine the time it takes for the watermelon to fall
Now, we need to find the time it takes for the watermelon to fall, as this will allow us to calculate the horizontal distance the car travels during that time.
Using the equation for vertical displacement, we can rearrange it as:
h = (1/2)gt²
Rearranging for time (t):
t = sqrt(2h/g)
Step 4: Calculate the horizontal distance traveled by the car
Now that we have the time it takes for the watermelon to fall (t), we can calculate the horizontal distance traveled by the car during that time. Since the car is moving at a constant velocity of 10 m/s, the horizontal distance (d) is given by:
d = vt
Substituting the known values:
d = 10 * t
Step 5: Calculate the lead distance
Finally, the lead distance (L) is the horizontal distance (d) that the car travels during the time it takes for the watermelon to fall. Therefore, we can substitute the previously calculated value of time (t) into the equation:
L = 10 * t
By following these steps and plugging in the values, you will be able to calculate the lead distance (L) required to drop the watermelon successfully into the manhole.