An egg is thrown from the top edge of a 22.9 m high building down onto an unsuspecting person standing on the ground 6.2 m from the base of the building. If the egg is tossed horizontally, at what speed, in m/s, must the egg be thrown such that it lands on the person?
y = 1/2gt^2
solve for t
x = vt
solve for v
To find the speed at which the egg must be thrown horizontally, we can use the following steps:
Step 1: Calculate the time it takes for the egg to fall from the top of the building to the ground.
We can use the formula for the time it takes for an object to fall:
t = sqrt(2h/g)
where:
- t = time (in seconds)
- h = height (in meters)
- g = acceleration due to gravity (approximately 9.8 m/s^2)
In this case, the height of the building is 22.9 m. Plugging in these values into the equation, we have:
t = sqrt(2 * 22.9 / 9.8)
Solving this equation will give us the time it takes for the egg to fall.
Step 2: Calculate the horizontal distance covered by the egg during this time.
Since the egg is thrown horizontally, there is no horizontal acceleration. Therefore, the horizontal distance covered is equal to the horizontal component of the egg's velocity multiplied by the time taken for it to fall.
The horizontal distance covered (d) can be determined using the formula:
d = v * t
where:
- d = horizontal distance (in meters)
- v = horizontal velocity (in meters per second)
- t = time (in seconds)
In this case, the horizontal distance is given as 6.2 m. We can rearrange the formula to solve for the horizontal velocity:
v = d / t
Plugging in the values for the horizontal distance and the time calculated in Step 1, we can find the required horizontal velocity.
Step 3: Calculate the speed of the egg.
The speed of the egg is calculated using the formula for the magnitude of velocity:
speed = sqrt(v^2 + u^2)
where:
- speed = magnitude of velocity (in meters per second)
- v = horizontal velocity (in meters per second)
- u = vertical velocity (in meters per second)
In this case, since the egg is thrown horizontally, the vertical velocity is 0 m/s. Thus, the speed simplifies to:
speed = |v|
In other words, the speed of the egg is equal to the magnitude of the horizontal velocity found in Step 2.
By following these steps, we can find the speed at which the egg must be thrown horizontally such that it lands on the person standing on the ground.