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 or any fruit 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 lead distance required to successfully drop the watermelon into the manhole, you need to consider two main factors:
1. The horizontal distance the car travels during the time it takes for the watermelon to fall from the initial height of 1 m to hit the manhole.
2. The horizontal distance the car needs to travel to align the manhole directly beneath the point where the watermelon is released.
Let's break down the calculations step by step:
Step 1: Calculate the time it takes for the watermelon to fall to the ground
The time for an object to fall vertically from a certain height can be determined using the formula:
t = √(2h/g)
Where:
t is the time in seconds
h is the height in meters
g is the acceleration due to gravity, which is approximately 9.8 m/s²
For the given initial height of 1 m:
t = √(2 * 1 / 9.8) ≈ 0.452 s
Step 2: Calculate the horizontal distance traveled by the car during the time of fall
Since the car is moving at a constant velocity, the horizontal distance traveled during the fall time can be calculated using the formula:
d = v * t
Where:
d is the distance in meters
v is the velocity of the car, which is 10 m/s (given)
t is the time calculated in Step 1
So, for the given velocity:
d = 10 m/s * 0.452 s ≈ 4.52 m
Step 3: Calculate the lead distance required
The lead distance required is the horizontal distance the car needs to travel to align the manhole beneath the point where the watermelon is released. Since the car is moving at a constant velocity, this lead distance depends on the time it takes for the watermelon to fall and the distance traveled by the car during that time.
Therefore, the lead distance can be calculated as:
lead distance = d / (2 * t)
Where:
d is the distance calculated in Step 2
t is the time calculated in Step 1
So, for the given values:
lead distance = 4.52 m / (2 * 0.452 s) ≈ 10.00 m
Therefore, in order to successfully drop the watermelon into the manhole, you should drop it approximately 10 meters ahead of the manhole.