(1)using the appropriate kinematics equation and the quadratic formula, compute

Question

(1)using the appropriate kinematics equation and the quadratic formula, compute the time it takes for a ball fired upwards at 274 m/s, from the ground, to reach 487 m for the first time.

Find the time it takes to reach 487 m in seconds. (round answer to 2 decimal places)

(2) Using the quadratic formula, compute the time it takes a ball fired upwards at 424 m/s, from the ground, to reach 401 m for the SECOND time.

Find the time it takes to reach 401 m in seconds. (round answer to 2 decimal places.)

Explanation / Answer

Q1. initial speed =274 m/s

assume that upward direction is positive.

then acceleration due to gravity=-9.8 m/s^2 (-ve sign because of the downward direction)

distance to be covered=487 m

let time taken for the same be t seconds.

using the formula,

distance=initial speed*time+0.5*acceleration*time^2

==>487=274*t-0.5*9.8*t^2

==>4.9*t^2-274*t+487=0

==>t=1.8377 seconds or 54.08 seconds

as we want to find out when it crosses 487 m for the first time, t=1.8377 seconds is the correct answer.

in two decimal places, answer=1.84 seconds

Q2. initial speed=424 m/s

height to be reached=401 m

let time taken be t seconds.

then 424*t-0.5*9.8*t^2=401

==>4.9*t^2-424*t+401=0

solving for t , we get85.5742 seconds or 0.9563 seconds

as we want to find out when the object crosses for the second stime,the higher of the two solutions i.e. 85.5742 seconds is the correct answer.

in 2 decimal places, answer=85.57 seconds

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