Question

Timothy, Prince of All the Land, shoots and arrow down from the ramparts of his castle. If he points his bow down at a 28° with the horizontal, and the castle wall is 140m tall, how far from the base of the wall will the arrow land?

Answer 1

To find the distance from the base of the wall where the arrow will land, we can use the concept of projectile motion and trigonometry calculations. We can use the formula for horizontal distance traveled in projectile motion to find the distance. The initial vertical position of the arrow plays a role in determining the time it takes for the arrow to reach the ground.

Step-by-step explanation:

To find the distance from the base of the wall where the arrow will land, we can use the concept of projectile motion. Given that the castle wall is 140m tall and Timothy shoots the arrow at a 28° angle with the horizontal, we need to determine the horizontal distance traveled by the arrow. We can use the trigonometric function cosine to find the horizontal component of the initial velocity of the arrow.

1. First, find the horizontal component of the initial velocity by multiplying the initial velocity by the cosine of the launch angle.
2. Next, use the formula for horizontal distance traveled in projectile motion, which is given by the equation: distance = initial velocity imes cos(angle) imes time.
3. Since the arrow is launched from the top of the wall, the initial vertical position is 140m. To find the time it takes for the arrow to reach the ground, we can use the formula for vertical displacement: displacement = (initial velocity imes sin(angle) imes time) + (0.5 imes acceleration imes time^2).
4. Finally, substitute the time found in the previous step into the horizontal distance formula to find the distance from the base of the wall where the arrow will land.