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A projectile is fired with an initial speed of 250m/s, angle of 60deg, at height of 110m.?
Multivariable Calculus
a) Find the range of the projectile
b) Maximum height
c) Speed at impact
So I found the y component to be [250(m/s)*sin(60) + 110m]
and assuming gravity is y=[-9.8(m/s^2)]
I set them equal to each other and solved for s and got [33.317s]
I then got the x comp as [250cos(60)] and multiplied it by [33.317s] and got [4164m],
This is not right and am not sure where to start...
1 Answer
- 8 years agoFavorite Answer
First, break its velocity vector down into position components, x and y, using a right triangle, calculus, and some common sense:
dy/dt=250*sin(60deg) - 9.8*t
integrate with respect to t to get equation for y, note that C=110 meters in this case
dx/dt=250*cos(60deg)
integrate with respect to t to get equation for x
Now that you have your two position functions, everything else is a piece of cake:
a) find t when y=0, pick the larger of the two solutions plug t-value into x equation to find range
b) find when dy/dt = 0 to get maximum height
c) plug t-value from part a into both velocity equations to get parameterized velocity at impact, then use pythagorean theorem to recombine them into vector form (dy/dt ^2 +dx/dt ^2 = dy/dx ^2 in this example)
