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svet-max [94.6K]
3 years ago
7

The position function for a free-falling object is s(t) = -16t^2 + vt +5. A ball is thrown upward from the top of a 400-foot bui

lding with an initial velocity of 35 feet per second. At what time will the ball reach the ground (round answer to nearest hundredths)? O at 2.19 seconds at 0 seconds at 6.21 seconds at -4.02 seconds
Mathematics
1 answer:
mixer [17]3 years ago
4 0

Answer:

6.21 seconds

Step-by-step explanation:

The position function of a free-falling object is,

s(t) = -16t^2+v_0t+s_0

Where,

s_0 = initial height of the object,

v_0 = initial velocity of the object,

Here,

s_0=400\text{ feet}

v_0=35\text{ feet per sec}

Hence, the height of the ball after t seconds,

s(t)=-16t^2+35t+400

When s(t) = 0,

\implies -16t^2+35t+400=0

t=\frac{-35\pm \sqrt{35^2-4\times -16\times 400}}{2\times -16}

t=\frac{-35\pm \sqrt{1225+25600}}{-32}

\implies t\approx -4.02\text{ or }t\approx 6.21

∵ Time cannot be negative,

Hence, after 6.21 seconds the ball will reach the ground.

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