Question

question 14
(problem reference 3 - 2) a projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
determine the initial speed of the projectile.

a. 40 m/s
b. 50 m/s
c. 10 m/s
d. 70 m/s

Explanation:

Step1: Recall speed - vector relation

The initial speed $v_0$ of a projectile with initial horizontal component of velocity $v_{0x}$ and initial vertical component of velocity $v_{0y}$ is given by the Pythagorean theorem since the horizontal and vertical velocity - components are perpendicular to each other. The formula is $v_0=\sqrt{v_{0x}^2 + v_{0y}^2}$.

Step2: Substitute given values

Given $v_{0x}=30\ m/s$ and $v_{0y}=40\ m/s$. Substitute these values into the formula: $v_0=\sqrt{30^{2}+40^{2}}=\sqrt{900 + 1600}=\sqrt{2500}$.

Step3: Calculate the result

$\sqrt{2500}=50\ m/s$.

Answer:

B. 50 m/s