To find out how long it takes for the object to fall 171 feet, we need to set the equation for the distance s equal to 171 and solve for time t.

The equation is s = 9t + 16t^2.

Setting s equal to 171 gives us:

171 = 9t + 16t^2.

This is a quadratic equation in the form of at^2 + bt + c = 0, where a = 16, b = 9, and c = -171.

We can solve this equation for t using the quadratic formula, which is t = [-b ± sqrt(b^2 - 4ac)] / (2a).

Substituting the values of a, b, and c into the formula gives us:

t = [-9 ± sqrt((9)^2 - 4*16*(-171))] / (2*16)
t = [-9 ± sqrt(81 + 10944)] / 32
t = [-9 ± sqrt(11025)] / 32
t = [-9 ± 105] / 32

This gives us two possible solutions: t = (105 - 9) / 32 = 3 seconds and t = (-105 - 9) / 32, which is a negative number and doesn't make sense in this context because time can't be negative.

So, it takes the object 3 seconds to fall 171 feet.

Question

To find out how long it takes for the object to fall 171 feet, we need to set the equation for the distance s equal to 171 and solve for time t.

The equation is s = 9t + 16t^2.

Setting s equal to 171 gives us:

171 = 9t + 16t^2.

This is a quadratic equation in the form of at^2 + bt + c = 0, where a = 16, b = 9, and c = -171.

We can solve this equation for t using the quadratic formula, which is t = [-b ± sqrt(b^2 - 4ac)] / (2a).

Substituting the values of a, b, and c into the formula gives us:

t = [-9 ± sqrt((9)^2 - 4*16*(-171))] / (2*16)
t = [-9 ± sqrt(81 + 10944)] / 32
t = [-9 ± sqrt(11025)] / 32
t = [-9 ± 105] / 32

This gives us two possible solutions: t = (105 - 9) / 32 = 3 seconds and t = (-105 - 9) / 32, which is a negative number and doesn't make sense in this context because time can't be negative.

So, it takes the object 3 seconds to fall 171 feet.

Knowee AI · Accepted Answer

To find out how long it takes for the object to fall 171 feet, we need to set the equation for the distance s equal to 171 and solve for time t.

The equation is s = 9t + 16t^2.

Setting s equal to 171 gives us:

171 = 9t + 16t^2.

This is a quadratic equation in the form of at^2 + bt + c = 0, where a = 16, b = 9, and c = -171.

We can solve this equation for t using the quadratic formula, which is t = [-b ± sqrt(b^2 - 4ac)] / (2a).

Substituting the values of a, b, and c into the formula gives us:

t = [-9 ± sqrt((9)^2 - 4*16*(-171))] / (2*16)
t = [-9 ± sqrt(81 + 10944)] / 32
t = [-9 ± sqrt(11025)] / 32
t = [-9 ± 105] / 32

This gives us two possible solutions: t = (105 - 9) / 32 = 3 seconds and t = (-105 - 9) / 32, which is a negative number and doesn't make sense in this context because time can't be negative.

So, it takes the object 3 seconds to fall 171 feet.

An object is thrown downward with an initial velocity of 9 feet per second. The relationship between the distance 𝑠 it travels and time 𝑡 is given by 𝑠=9⁢𝑡+16⁢𝑡2. How long does it take the object to fall 171 feet?It takes second(s) for the object to fall 171 feet.

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