In Denver, children bring their old jack-o-lanterns to the top of a tower and compete for accuracy in hitting a target on the ground. Suppose that the tower height is h = 9.80 m, and that the bulls-eye is a horizontal distance of d = 3.2 m from the launch point. If the pumpkin is thrown horizontally, what is the launch speed needed to hit the bulls-eye? (Neglect air resistance.)
To find the launch speed needed to hit the bulls-eye, we can use the following equation of motion:
d = v₀ * t
where:
d is the horizontal distance (3.2 m in this case),
v₀ is the initial velocity (launch speed),
and t is the time taken for the pumpkin to reach the target.
In this case, the initial vertical velocity is zero because the pumpkin is thrown horizontally. We can find the time taken for the pumpkin to fall from the tower height by using the following kinematic equation:
h = (1/2) * g * t²
where:
h is the height of the tower (9.80 m),
g is the acceleration due to gravity (usually taken as 9.8 m/s²),
and t is the time of flight.
Solving this equation for t, we get:
t = sqrt((2 * h) / g)
Plugging in the values, we have:
t = sqrt((2 * 9.80) / 9.8) = 2 s
Now that we have the time of flight, we can substitute it back into the first equation to find the launch speed:
d = v₀ * t
3.2 = v₀ * 2
Dividing both sides by 2:
v₀ = 3.2 / 2 = 1.6 m/s
Therefore, the launch speed needed to hit the bulls-eye is 1.6 m/s.
S=d/t
9-3.5=5.5