You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity
v
at an angle θ with respect to the horizontal. Let the building be 49.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 11.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released.
What is the question?
To solve the projectile motion problem, we can break down the initial velocity into horizontal and vertical components. The initial horizontal velocity is given as 9.00 m/s, so vx = 9.00 m/s.
The initial vertical velocity is given as 11.5 m/s, and the positive y-axis is upward. Hence, vy = 11.5 m/s.
Now, we can use the equations of motion to determine various parameters of the projectile's motion.
1. Time of flight (t):
The time taken by the ball to reach the ground can be calculated using the equation:
t = 2 * vy / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values into the equation:
t = 2 * 11.5 m/s / 9.8 m/s²
t ≈ 2.35 s
2. Horizontal distance traveled (dx):
The horizontal distance traveled by the projectile can be calculated using the equation:
dx = vx * t
where vx is the initial horizontal velocity, and t is the time of flight.
Substituting the given values into the equation:
dx = 9.00 m/s * 2.35 s
dx ≈ 21.15 m
3. Maximum height (h):
The maximum height reached by the projectile can be determined using the equation:
h = (vy^2) / (2 * g)
where vy is the initial vertical velocity, and g is the acceleration due to gravity.
Substituting the given values into the equation:
h = (11.5 m/s)^2 / (2 * 9.8 m/s²)
h ≈ 6.25 m
By choosing the coordinate system with the positive y-axis upward and the x-axis to the right, we have correctly determined the time of flight, horizontal distance traveled, and maximum height of the projectile. Thus, this example demonstrates the flexibility of using any suitable coordinate system in solving projectile motion problems.