Question

A gazelle runs past a cheetah crouching below the grass on the planes of the savanna. When the gazelle is 4.00m past the cheetah, the cheetah begins to accelerate from rest at a rate of 12.0 m/s2 toward the running gazelle. The gazelle runs at a constant speed of 14.0 m/s. a. How much time does it take the cheetah to reach the gazelle after beginning to accelerate? b. How far does the cheetah run before reaching the gazelle? c. How fast is the cheetah moving when it reaches the gazelle?

          A gazelle runs past a cheetah crouching below the grass on the
planes of the savanna. When the gazelle is 4.00m past the cheetah,
the cheetah begins to accelerate from rest at a rate of 12.0
m/s2 toward the running gazelle. The gazelle runs at a
constant speed of 14.0 m/s.
a. How much time does it take the cheetah to reach the gazelle
after beginning to accelerate?
b. How far does the cheetah run before reaching the gazelle?
c. How fast is the cheetah moving when it reaches the gazelle?
        
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Added by Aaron J.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A gazelle runs past a cheetah crouching below the grass on the planes of the savanna. When the gazelle is 4.00m past the cheetah, the cheetah begins to accelerate from rest at a rate of 12.0 m/s2 toward the running gazelle. The gazelle runs at a constant speed of 14.0 m/s. a. How much time does it take the cheetah to reach the gazelle after beginning to accelerate? b. How far does the cheetah run before reaching the gazelle? c. How fast is the cheetah moving when it reaches the gazelle?
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Transcript

-
00:01 Hello, here we have to solve the following problem.
00:02 When the gazelle is 4 meters past the cheetah, the cheetah begins to accelerate at rest, from rest at the rate of 12 meters per square second, and the gazelle runs at a constant speed of 14 meters per second.
00:22 Here we have to determine how much time it takes for chita to reach the gazelle.
00:29 So let's do this.
00:31 First, let's write down x equation.
00:33 For coordinate of gazelle that is delta x plus speed of gazelle times time and x coordinate of the cheetah is acceleration of cheetah over 2 times t squared when the cage happens x of gazelle becomes equals to x of cheetah and now we can substitute parameters with numbers 60 squared minus 14 t minus 4 equals to 0 let's divide both all equation by 2 and now let's calculate the discriminate that is 49 plus 3 times 2 times 4 let's complete this calculation that is 73 and now we can determine time so that is 7 plus square root of 73 over 6 seconds that's 2 .59 seconds.
02:07 Now in question b we have to calculate speed of cheetah when it catches a gazelle so that's acceleration of cheetah times time t that is 31 .1 meters per second.
02:31 Oh actually here that's basically answer to question c so that's the speed of the cheetah and now let's answer question b...
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