Answer:
4.06 seconds
148.3 meters
Step-by-step explanation:
To solve for the time it takes for the projectile to hit the ground, we can use the following kinematic equation:
y = y_0 + v_0y * t + 1/2 * a_y * t^2
where y is the final height (0 m), y_0 is the initial height (also 0 m), v_0y is the initial vertical velocity, and a_y is the acceleration due to gravity (-9.8 m/s^2).
First, we need to find v_0y, the initial vertical velocity:
v_0y = v_0 * sin(theta) = 42 m/s * sin(28 degrees) ≈ 19.6 m/s
Now, we can solve for the time it takes to hit the ground:
0 = 0 + 19.6 m/s * t + 1/2 * (-9.8 m/s^2) * t^2
Simplifying and solving for t, we get:
t ≈ 4.06 seconds
Therefore, it takes about 4.06 seconds for the projectile to hit the ground.
To find the horizontal distance traveled by the projectile, we can use the following kinematic equation:
x = v_0x * t
where x is the horizontal distance traveled, v_0x is the initial horizontal velocity, and t is the time it takes to hit the ground (which we just calculated).
Since there is no air resistance, the horizontal velocity remains constant throughout the motion. Therefore:
v_0x = v_0 * cos(theta) = 42 m/s * cos(28 degrees) ≈ 36.5 m/s
Now, we can plug in the values to find the horizontal distance traveled:
x = 36.5 m/s * 4.06 s ≈ 148.3 meters