Final answer:
The maximum height and horizontal distance of a projectile fired at a certain angle and speed are calculated using the initial velocity's horizontal and vertical components to find the time of flight, and then using that to determine the height and range.
Step-by-step explanation:
To find the maximum height and horizontal distance a projectile will travel, we first decompose the initial velocity into its horizontal and vertical components. For a projectile fired at an angle θ with an initial speed v, the horizontal and vertical components of the initial velocity (vx and vy respectively) are given by:
- vx = v × cos(θ)
- vy = v × sin(θ)
The maximum height (H) is reached when the vertical component of the velocity becomes zero. The formula to find this height using the initial vertical velocity (vy) and the acceleration due to gravity (g) is:
H = (vy²) / (2g)
To find the horizontal range (R), also known as the projectile's displacement, we need the time of flight. It can be obtained from the vertical motion equations and is equal to:
T = 2 × vy / g
The horizontal distance is then:
R = vx × T
Substituting the values for an initial speed of 150 m/s and an angle of 47°, we can find the maximum height and range of the projectile.