A particle travels horizontally between two parallel walls separated by 18.4 m. It moves toward the opposing wall at a constant rate of 9.8 m/s. Also, it has an acceleration in the direction parallel to the walls of 3.7 m/s2.At what angle with the wall will the particle strike?
Answer in units of ◦
To find the angle at which the particle will strike the wall, we need to use trigonometry. Let's break down the problem into components:
1. The horizontal distance traveled by the particle is 18.4 m.
2. The particle's initial velocity in the horizontal direction is 9.8 m/s.
3. The particle's acceleration in the horizontal direction is 3.7 m/s^2.
Let's find the time it takes for the particle to hit the wall. We can use the formula:
distance = initial velocity * time + 0.5 * acceleration * time^2
18.4 m = 9.8 m/s * time + 0.5 * 3.7 m/s^2 * time^2
Rearranging this equation to solve for time, we get:
0.5 * 3.7 m/s^2 * time^2 + 9.8 m/s * time - 18.4 m = 0
Solving this quadratic equation, we find that time ≈ 1.588 seconds.
Now, let's find the vertical distance the particle travels during this time. Since the particle is moving horizontally, the vertical distance traveled can be calculated using the equation:
vertical distance = 0.5 * acceleration * time^2
vertical distance = 0.5 * 3.7 m/s^2 * (1.588 s)^2 ≈ 4.679 m
Next, we can use the vertical distance and the horizontal distance traveled by the particle to find the angle at which it will strike the wall. The angle can be calculated using the trigonometric relationship:
tan(angle) = vertical distance / horizontal distance
tan(angle) = 4.679 m / 18.4 m
angle ≈ arctan(4.679 m / 18.4 m)
Using a calculator, we find that the angle is approximately 14.7 degrees.
Therefore, the particle will strike the wall at an angle of approximately 14.7 degrees.