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LuckyWell [14K]
4 years ago
16

The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the

object is 150 feet. After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds
Physics
2 answers:
Rainbow [258]4 years ago
6 0

Answer:

3 seconds

Explanation:

Since h(t) represents the height and t represents the time, we can set the equation equal to 150 to find t.

-16t^2+96t+6=150

Subtract 150 from both sides to set the equation equal to 0, to find the solutions.

-16t^2+96t-144=0

Factor out -16, because all of the terms are divisible by it.

-16(t^2+6t+9)=0

Now we can focus on the terms inside the parenthesis and factor it again.

t^2-6t+9=0

We need to find two value that can be multiplied to get 9 and added to get -6.

-3 and -3 works.

Thus, we get (x-3)(x-3).

Now solve for 0.

x-3=0

x=3

The object reaches its maximum height after 3 seconds.

svp [43]4 years ago
6 0

Answer:

3 seconds

Explanation:

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Superman's initial velocity is v_{0}=54.5\frac{m}{s}, and he will have to cover a distance d = 850m in a time t = 4.22s. Since we know d, v_{0} and t, we have to find the aceleration a in order to find v_{f}.

From the equation d=v_{0} t+\frac{at^{2} }{2} we have to clear a, getting the equation as follows: a=\frac{2(d-v_{0}t) }{t^{2} }.

Substituting the values:

a=\frac{2(850m-54.5\frac{m}{s}.4.22s) }{(4.22s)^{2}}=69.63\frac{m}{s^{2}}

To find v_{f} we use the equation v_{f} =v_{0} +at.

Substituting the values:

v_{f} =54.5\frac{m}{s} +(69.63\frac{m}{s^{2}}.4.22s)=348.34\frac{m}{s}

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The slider of mass m is released from rest in position A and slides without friction along the vertical-plane guide shown. Deter
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The value of normal force as the slider passes point B is

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The value of h when the normal force is zero

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<h3>How to solve for the normal force</h3>

The normal force is calculated using the work energy principle which is applied as below

K₁ + U₁ = K₂

k represents kinetic energy

U represents potential energy

the subscripts 1,2 , and 3 = a, b, and c

for 1 to 2

K₁ + W₁ = K₂

0 + mg(h + R) = 0.5mv²₂

g(h + R) = 0.5v²₂

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Using summation of forces at B

Normal force, N  = ma + mg

N = m(a + g)

N = m(v²₂/R + g)

N = m(5gR/R + g)

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for 1 to 3

K₁ + W₁ = K₃ + W₃

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gh = 0.5v²₃ + gR

0.5v²₃ = gh - gR

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at C

for normal force to be zero

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v²₃/R = g

v²₃ = gR

and v²₃ = 2g(h - R)

gR = 2gh - 2gR

gR + 2gR = 2gh

3gR = 2gh

3R/2 = h

Learn more about normal force at:

brainly.com/question/20432136

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