Question

A dart is thrown horizontally at a target's center that is 5.00 m away. The dart hits the target 0.150 m below the target's center. We can ignore air resistance. What was the initial horizontal velocity of the dart?

Answer 1

The initial horizontal velocity of the dart needed to hit a target 5.00 m away and 0.150 m below its center, while ignoring air resistance, is approximately 28.57 m/s. This was determined by using the equations of motion for vertical displacement to find the time in air and then solving for the horizontal velocity using the horizontal displacement and time.

Step-by-step explanation:

The subject of this question is Physics. The problem is a classic example of projectile motion, where a dart is thrown horizontally and we are asked to determine its initial horizontal velocity. We need to use the equations of motion to solve for the time the dart is in the air and then use that time to find its initial velocity.

To find the time the dart is in the air, we use the equation for the vertical displacement under constant acceleration due to gravity (g = 9.81 m/s2):

Vertical displacement (s) = (1/2)gt2

We know that the vertical displacement s = 0.150 m, so we can solve for t (time):

s = (1/2)gt2

0.150 m = (1/2)(9.81 m/s2)t2

t2 = 2(0.150 m) / (9.81 m/s2)

t2 = 0.0306 s2

t ≈ 0.175 s

Now we calculate the initial horizontal velocity (vx) using the horizontal displacement and the time:

Horizontal displacement (x) = vxt

5.00 m = vx(0.175 s)

vx = 5.00 m / 0.175 s

vx ≈ 28.57 m/s

The initial horizontal velocity of the dart was approximately 28.57 m/s in order to hit the target 5.00 m away and 0.150 m below its center.