a projectile returns to its original height after 4.08 seconds, during which tie it travels 6.2 meters horizontally. If air resistance is ignored, what was the projectile's initial speed?

Question

a projectile returns to its original height after 4.08 seconds, during which tie it travels 6.2 meters horizontally. If air resistance is ignored, what was the projectile's initial speed?

Answer 1

Why did the projectile come back to its original height? Because it forgot its keys and had to turn back! Hilarious, right? Now, let's calculate its initial speed.

To find the initial speed, we'll use the fact that the time taken to reach the maximum height is the same as the time taken to return to the original height (assuming no air resistance). So, the total time of flight is 4.08 seconds.

Now, the horizontal distance traveled by the projectile (6.2 meters) is related to its initial velocity. We can use the formula:

distance = velocity * time

Therefore, we have:

6.2 = velocity * 4.08

Now, solve for velocity:

velocity = 6.2 / 4.08

Calculating this gives us:

velocity ≈ 1.5196 meters per second

So, the projectile's initial speed is approximately 1.5196 meters per second. Remember, this is all assuming that air resistance is ignored.

Answer 2

To find the initial speed of the projectile, we can use the formula for horizontal distance traveled by a projectile with constant velocity:

Horizontal distance = initial velocity * time

In this case, we know that the horizontal distance traveled is 6.2 meters and the time taken is 4.08 seconds. Let's substitute these values into the formula:

6.2 = initial velocity * 4.08

To solve for the initial velocity, we need to isolate it on one side of the equation. Divide both sides of the equation by 4.08:

initial velocity = 6.2 / 4.08

Calculating this, we find:

initial velocity ≈ 1.52 meters per second

Therefore, the projectile's initial speed is approximately 1.52 meters per second.

Answer 3

To find the initial speed of the projectile, we can use the formula for horizontal distance traveled by a projectile:

d = v₀ * t

where:
d = horizontal distance (6.2 meters)
v₀ = initial speed (what we want to find)
t = time (4.08 seconds)

Rearranging the formula, we have:

v₀ = d / t

Plugging in the values, we get:

v₀ = 6.2 meters / 4.08 seconds

Using a calculator, we can divide 6.2 by 4.08 to find the value of v₀, which is the initial speed of the projectile.

Answer 4

horizontal velocity (vh) = 6.2 m / 4.08 s

initial vertical velocity (vv)
... = (4.08 s / 2) * g

(initial speed)^2 = vh^2 + vv^2