Romeo's Pebbles - A Zero Horizontal Acceleration Problem

[EcKoh]

Homework Statement

Romeo is chucking pebbles as gently as he can up to Juliet's window. That is, he wants the pebbles to hit the wendow with the least possible speed. He is standing at the edge of a rose garden at D_v = 7.90 m below her window and at D_h = 8.50 m from the base of the wall. How fast are the pebbles going when they hit her window?

Homework Equations

V_f = V_i + ad_v (to find initial velocity)
V_f = V_i + at (to find hang time)
D_h = V_ht (to find constant horizontal velocity)

The Attempt at a Solution

Okay so I'm assuming I did everything right, so I'm not sure where I went wrong but here are the steps I took in my attempt:

3.1: List knowns and unknowns:

Knowns:
V_f = 0 m/s
a = -9.8 m/s₂
D_v = 7.90 m
D_H = 8.50 m

Unknowns:
V_i = ?

3.2: Find the initial velocity:

V_f = V_i + ad_v
(0) = V_i + (-9.8)(7.90)
V_i = 77.42

3.3: Find hang time:

V_f = V_i + at
(0) = (77.42) + (-9.8)t
-77.42 = -9.8t
t = 7.9s <-- (maybe I went wrong here? I noticed that's the same as D_v

3.4: Find constant velocity:

D_h = V_ht
(8.50) = V_h(7.9)
V_h = 1.08

So 1.08 m/s turns out to be the wrong answer, and I keep going back and reworking it but I'm not sure what I'm doing wrong. Its due online tonight in just a few hours, but either way it's driving me crazy so I just want to know what I'm doing wrong and how to fix it.

Thanks!

 

[rl.bhat]

Hi EcKoh, welcome to PF.
In the relevant equations, the first equation is wrong. Check that.

 

[faradayslaw]

Yes, vf != v0 + ad, rather, v^2 = v0^2 +2ad

 

[kuruman]

What you are doing wrong is treat this two dimensional problem as if it were one-dimensional. You need to write the vertical and horizontal equations of motion. Then you need to consider at what part of the trajectory the speed is a minimum. Also, your equation
v_f=v_i+ad_v is incorrect.

 

[EcKoh]

Thanks guys, I corrected the formula and was able to get a correct answer of 6.69 m/s