Now that you have the equation for your projectile, use it to calculate how far from the launcher the projectile
landed.

Ask by Bartlett Salazar. in the United States

Jan 13,2025

Question

Now that you have the equation for your projectile, use it to calculate how far from the launcher the projectile landed. $$ y=-4,13(x-1,5)^{2}+16.97 $$

UpStudy AI · Accepted Answer

To determine how far from the launcher the projectile landed, we need to analyze the given parabolic equation:

$$
y = -4{,}13(x - 1{,}5)^2 + 16{,}97
$$

**Step 1: Interpret the Equation**

- Here, $$ y $$ represents the vertical position (height) of the projectile.
- $$ x $$ represents the horizontal position (distance) from a reference point.

**Step 2: Determine the Landing Point**

The projectile lands when its height $$ y = 0 $$. Set the equation to zero and solve for $$ x $$:

$$
0 = -4{,}13(x - 1{,}5)^2 + 16{,}97
$$

$$
4{,}13(x - 1{,}5)^2 = 16{,}97
$$

$$
(x - 1{,}5)^2 = \frac{16{,}97}{4{,}13} \approx 4{,}11
$$

$$
x - 1{,}5 = \pm \sqrt{4{,}11} \approx \pm 2{,}028
$$

$$
x \approx 1{,}5 \pm 2{,}028
$$

So, the two possible $$ x $$ values are:

$$
x_1 \approx 1{,}5 + 2{,}028 = 3{,}528 \, \text{meters}
$$
$$
x_2 \approx 1{,}5 - 2{,}028 = -0{,}528 \, \text{meters}
$$

**Step 3: Calculate the Distance from the Launcher**

Assuming the launcher is at the origin $$ (0, 0) $$, the relevant landing point is $$ x \approx 3{,}528 $$ meters (we discard the negative value as distance cannot be negative).

However, considering the vertex of the parabola is at $$ x = 1{,}5 $$, the total horizontal distance traveled (range) is:

$$
\text{Total Range} = 3{,}528 - (-0{,}528) = 4{,}056 \, \text{meters}
$$

**Conclusion**

The projectile landed approximately **4,06 meters** from the launcher.
The projectile landed approximately 4,06 meters from the launcher.

Now that you have the equation for your projectile, use it to calculate how far from the launcher the projectile
landed.

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