Question

Malq designed a model catapult for a school science competition. The first projectile he launched landed 188 feet from the catapult.

He rotated the catapult 41 to the left, and fired another projectile. This projectile landed 112 feet from the catapult
What is the approximate distance between landing sites?

Answer 1

To find the approximate distance between the landing sites, we can use trigonometry to calculate the horizontal displacement for each projectile. The approximate distance is 103.48 feet.

Step-by-step explanation:

To find the approximate distance between the landing sites, we need to calculate the horizontal displacement for each projectile. The first projectile landed 188 feet from the catapult, and the second projectile landed 112 feet from the catapult after rotating 41 degrees to the left.

To calculate the approximate distance between the landing sites, we can use trigonometry. The horizontal displacement is given by the formula:

Horizontal Displacement = Initial Velocity x Cos(Angle)

For the first projectile: Horizontal Displacement1 = 188 x Cos(0) = 188 feet

For the second projectile: Horizontal Displacement2 = 112 x Cos(41) = 84.52 feet

Therefore, the approximate distance between the landing sites is approximately 188 - 84.52 = 103.48 feet.

Answer 2

Step-by-step explanation:

We can use the Pythagorean theorem to calculate the distance between the two landing sites. Let's call this distance "d".

First, we need to calculate the horizontal and vertical components of the distance traveled by each projectile. Let's call the horizontal component "x" and the vertical component "y".

For the first projectile, the horizontal component is 188 feet (since it landed directly in front of the catapult), and the vertical component is 0 feet (since it didn't go up or down).

For the second projectile, we need to use trigonometry to calculate the horizontal and vertical components. The angle of rotation is 41 degrees, and the distance traveled is 112 feet. So:

x = 112 * cos(41) ≈ 83.2 feet

y = 112 * sin(41) ≈ 71.5 feet

Now we can use the Pythagorean theorem to calculate the distance between the landing sites:

d = sqrt((188 - 83.2)^2 + (0 - 71.5)^2) ≈ 123.5 feet

So the approximate distance between the landing sites is 123.5 feet.