How many seconds will the ball be going upward if a ball is thrown vertically upward from the ground with an initial velocity of 20 feet per second and #a(t)= -32# feet per second squared?

Answer 1
The ball will continue to go upward until its (upward) velocity #= 0#

The ball's upward velocity is the sum of its initial upward velocity plus its upward velocity (really minus its downward velocity) due to gravity.

This velocity will #=0# for a time #t# (in seconds) when #0 = (20 ft)/(sec) + (-32 ft)/(sec^2)* t sec#
This simplifies to # t = 5/8 sec.#
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Answer 2

To determine the time the ball will be going upward, you can use the following kinematic equation:

[v_f = v_i + a t]

Where:

  • (v_f) is the final velocity (which will be 0 when the ball reaches its peak)
  • (v_i) is the initial velocity (20 feet per second)
  • (a) is the acceleration due to gravity (-32 feet per second squared)
  • (t) is the time

Rearranging the equation to solve for (t), we get:

[t = \frac{v_f - v_i}{a}]

Since the final velocity ((v_f)) at the peak of the motion is 0, we have:

[0 = 20 - 32t]

Solving for (t), we find:

[t = \frac{20}{32}]

[t = 0.625] seconds

So, the ball will be going upward for approximately 0.625 seconds.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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