Can I use a dot product of accel. and vel. to find displace.

AI Thread Summary
To determine the initial speed of a projectile ejected at 35 degrees to reach a horizontal distance of 9.4 km and a vertical drop of 3.3 km, the dot product of velocity and acceleration is considered. The resultant displacement is calculated to be 9.96 km, leading to the equation v⋅a=vacos55, where the angle between acceleration and velocity is 55 degrees. This results in an initial speed of approximately 1736.5 m/s. The discussion highlights the importance of recognizing displacement as a vector in the calculations. Clarification on the use of the dot product in this context is sought for further understanding.
Jamiemma1995
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Homework Statement

at what initial speed would a projectile have to start at when ejected at 35 degrees to the horizontal from a point A to a point B which is 9.4km distance away in the horizontal and 3.3km below it. taking g as 10m/s[/B]

Homework Equations


I'm not really sure if these equations are relevant because if I can't use the dot product they are not

A⋅B=ABcosθ

The Attempt at a Solution

so first of all the resultant displacement between the x and y is 9.96 km so the I said that v⋅a=vacos55 (as the angle between the acceleration which is straight down and v is 55) and because I'm assuming that the dot product between v and a is displacement I said 9960=v10cos55 and got v=1736.5 m/s[/B]
 
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I just realized of course displacement is also a vector, which was pretty silly of me still any help with the actual question would be much appreciated
 

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