Juliet sits on her balcony while Romeo serenades her from the ground, 7.00m below. To win Juliet’s affection, Romeo throws Juliet a bouquet of roses. At what velocity must the roses be thrown if they are to reach Juliet on the balcony?.
To find the velocity at which the roses must be thrown in order to reach Juliet on the balcony, we can use the kinematic equation:
vf^2 = vi^2 + 2aΔd
Where:
- vf is the final velocity of the roses when they reach Juliet's balcony
- vi is the initial velocity at which the roses are thrown
- a is the acceleration due to gravity, which is approximately 9.8 m/s^2
- Δd is the vertical distance between Romeo on the ground and Juliet on the balcony, which is 7.00m in this case
Since the roses are thrown from the ground, the initial velocity is 0 (vi = 0). The final velocity (vf) will be the velocity we want to find.
We can rearrange the equation to solve for vf:
vf^2 = vi^2 + 2aΔd
Since vi is 0, this simplifies to:
vf^2 = 2aΔd
Substituting the values we know:
vf^2 = 2 * 9.8 m/s^2 * 7.00 m
Simplifying further:
vf^2 = 137.2 m^2/s^2
To find vf, we take the square root of both sides:
vf = √137.2 m^2/s^2
vf ≈ 11.7 m/s
Therefore, the roses must be thrown with a velocity of approximately 11.7 m/s in order to reach Juliet on the balcony.
v^2 = 2gy
v = sqrt(2*9.8*7)