Solve this physics based on the topic projectile motion

Question

ScanSolve AI Tutor · Accepted Answer

To find the maximum height reached by the projectile, we use the formula for maximum height in projectile motion.

Identify the given values.
Initial velocity, $v_0 = 20 \text{ m/s}$
Launch angle, $\theta = 30^\circ$
Acceleration due to gravity, $g = 9.8 \text{ m/s}^2$
Use the formula for maximum height ( $H$ ).
The formula for maximum height is:
$H = \frac{v_0^2 \sin^2 \theta}{2g}$
Substitute the values into the formula and calculate.
First, calculate $\sin 30^\circ$ :
$\sin 30^\circ = 0.5$
Now, substitute the values:
$H = \frac{(20 \text{ m/s})^2 (\sin 30^\circ)^2}{2 \times 9.8 \text{ m/s}^2}$ $H = \frac{(20)^2 (0.5)^2}{19.6}$ $H = \frac{400 \times 0.25}{19.6}$ $H = \frac{100}{19.6}$ $H \approx 5.102 \text{ m}$
Compare the result with the given options.
The calculated maximum height is approximately $5.1 \text{ m}$ . This matches option A.

The correct option is A.
The maximum height reached by the projectile is $\boxed{\text{A. } 5.1 \text{ m}}$ .

Answer