PHYSICS: The velocity vector of a sprinting cheetah has x- and y-components vx = +14.5 m/s and vy = -25.3 m/s?
The velocity vector of a sprinting cheetah has x- and y-components vx = +14.5 m/s and vy = -25.3 m/s
(a) What is the magnitude of the velocity vector? (in m/s)
(b) What angle does the velocity vector make with the +x- and −y-axes? (in _____ ° with the +x-axis and in ____ ° with the −y-axis)
Please explain what equation was used and show STEP BY STEP! I have the answers, I need to understand how it is solved!!
answer for a) is 29.2 m
answer for b) is 60.2° with the +x-axis and 29.8° with the -y-axis
The velocity vector of a sprinting cheetah has x- and y-components vx = +14.5 m/s and vy = -25.3 m/s
(a) What is the magnitude of the velocity vector? (in m/s)
(b) What angle does the velocity vector make with the +x- and −y-axes? (in _____ ° with the +x-axis and in ____ ° with the −y-axis)
Please explain what equation was used and show STEP BY STEP! I have the answers, I need to understand how it is solved!!
answer for a) is 29.2 m
answer for b) is 60.2° with the +x-axis and 29.8° with the -y-axis
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a) well you have the x and y components of the velocity so all you need to do is treat it like a triangle and use Pythagorean theorem to get the velocity. so it is the SQUARE ROOT of vx^2 +vy^2.
b) For this part you need to do some trig. remember that the tangent of an angle is equal to the opposite component divided by the adjacent component. so to get the angle with the x axis, do the INVERSE tangent of (vy/vx). that will give you the angle to the x axis. Then to find the angle with the Y axis simply subtract it from 90. so 90-(angle with x axis)= angle with y axis
b) For this part you need to do some trig. remember that the tangent of an angle is equal to the opposite component divided by the adjacent component. so to get the angle with the x axis, do the INVERSE tangent of (vy/vx). that will give you the angle to the x axis. Then to find the angle with the Y axis simply subtract it from 90. so 90-(angle with x axis)= angle with y axis
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Drawing this question out will probably help. They have given you the magnitude of the cheetah's velocity in both the x-direction and the y-direction. If you draw out your x-axis and y-axis with their respective values, you can find the resultant vector of the two by drawing a line which connects these two components. Doing this gives you a triangle.
With our triangle we can use pythagoreas' theorem to find out what the velocity vector's magnitude is.
Pythagoreas' Theorem: a^2+b^2=c^2
Plugging in the numbers to find our vector (c):
(14.5)^2+(-25.3)^2=c^2
(210.25)+(640.09)=c^2
√(850.34)=√(c^2)
29.16...=c
So your velocity vector would have a magnitude of 29.2 m/s
In part b) you'll need to use your knowledge of trigonometry to find the two angles.
I'll let you work on that since its kind of tough to show without a diagram.
Good Luck!
With our triangle we can use pythagoreas' theorem to find out what the velocity vector's magnitude is.
Pythagoreas' Theorem: a^2+b^2=c^2
Plugging in the numbers to find our vector (c):
(14.5)^2+(-25.3)^2=c^2
(210.25)+(640.09)=c^2
√(850.34)=√(c^2)
29.16...=c
So your velocity vector would have a magnitude of 29.2 m/s
In part b) you'll need to use your knowledge of trigonometry to find the two angles.
I'll let you work on that since its kind of tough to show without a diagram.
Good Luck!