A dart is being thrown at a board that is 3.40 m away. When it hits the board it is 0.784 m below the point where it was aimed and it was thrown at 8.50 m/s. How long was the dart in the air?
d = 0.5g*t^2 = 0.784.
4.9*t^2 = 0.784,
t = 0.4 s. = Time in air.
Well, this dart seems to be one skilled acrobat! Let's calculate the time it took for this daredevil dart to reach its target.
We can start by breaking down the motion of the dart into horizontal and vertical components. Since we're only concerned with the vertical displacement, let's focus on that.
The vertical displacement is given as -0.784 m (negative because it's below the aimed point) and the initial vertical velocity is zero (assuming it's thrown horizontally, without any initial upward or downward velocity).
Using the kinematic equation for vertical displacement:
Δy = V₀y * t + (1/2) * a * t²
where:
Δy = vertical displacement = -0.784 m (negative because it's below the aimed point)
V₀y = initial vertical velocity = 0 m/s
a = acceleration due to gravity = -9.8 m/s² (negative because it acts downward)
t = time
Rearranging the equation and solving for t:
-0.784 = (1/2) * (-9.8) * t²
-0.784 = -4.9 * t²
Dividing both sides by -4.9:
t² = 0.160
Taking the square root of both sides:
t ≈ 0.4 s
So, the dart was in the air for approximately 0.4 seconds. Keep practicing your aim, and who knows, maybe you'll hit the bullseye next time!
To find the time the dart was in the air, we can use the equations of motion. We know the initial vertical displacement (0.784 m) and the initial vertical velocity (0 m/s). The acceleration due to gravity is 9.8 m/s^2, pointing downwards.
The equation we can use is:
Displacement = Initial Velocity * Time + (1/2) * Acceleration * Time^2
For vertical motion, we can set the equation as:
-0.784 m = 0 m/s * t + (1/2) * (-9.8 m/s^2) * t^2
Simplifying the equation:
-0.784 m = -4.9 m/s^2 * t^2
Now, rearrange the equation to solve for t:
t^2 = (-0.784 m) / (-4.9 m/s^2)
Dividing both sides by -4.9 m/s^2:
t^2 = 0.16 s
Taking the square root of both sides:
t ≈ 0.4 s
Hence, the dart was in the air for approximately 0.4 seconds.