To find the maximum height reached by the projectile, you can use the following steps:
Step 1: Resolve the initial velocity into its horizontal and vertical components. The initial velocity (V) of the projectile is 40 m/s, and it is projected at an angle of 30° to the horizontal. To find the vertical and horizontal components, you can use the following equations:
V_vertical = V * sin(θ) V_horizontal = V * cos(θ)
where: V_vertical is the vertical component of the velocity, V_horizontal is the horizontal component of the velocity, and θ is the angle of projection (30°).
Substituting the values, we get: V_vertical = 40 m/s * sin(30°) V_horizontal = 40 m/s * cos(30°)
Step 2: Determine the time taken to reach the highest point. At the highest point of the projectile's trajectory, the vertical component of its velocity becomes zero. This happens because the projectile's motion changes from going upward to coming back down. The time taken to reach the highest point can be determined using the formula:
V_vertical = V_initial_vertical + (g * t)
where: V_vertical is the vertical component of velocity (0 m/s at the highest point), V_initial_vertical is the initial vertical component of velocity (V_vertical calculated earlier), g is the acceleration due to gravity (approximately 9.8 m/s²), t is the time taken to reach the highest point.
Using the formula, we can rearrange it to solve for t:
t = -V_initial_vertical / g
Substituting the values, we get: t = -(40 m/s * sin(30°)) / 9.8 m/s²
Step 3: Calculate the maximum height. The maximum height reached by the projectile can be found using the formula:
h_max = V_initial_vertical * t + (0.5 * g * t²)
Substituting the values, we get: h_max = (40 m/s * sin(30°)) * (-(40 m/s * sin(30°)) / 9.8 m/s²) + (0.5 * 9.8 m/s² * (-(40 m/s * sin(30°)) / 9.8 m/s²)²)
Simplifying the equation will give you the maximum height reached by the projectile.