H = –16t2 + 156t + 105, when t = t', the time where the rocket hit the ground after it is launched, so 105= –16t'2 + 156t' + 105, so -16t'2 + 156t' = 0 implies t' =0 or -16t'+ 156= 0, equivalent to t'=9.75, so the answer is
b) <span>9.8 s</span>
Answer:
a. 2.56 sec
b. 65.96 feet.
Step-by-step explanation:
a) The equation of motion of a body under gravity gives the equation
......... (1) {Where u is the initial velocity of the body and t is the time to descend h height and g is the acceleration due to gravity.
Now, from the equation (1) we have
{Since g = 32 feet/sec² }
⇒
So, applying Sridhar Acharya formula
seconds {Neglecting the negative root as t can not be negative.} (Answer)
b) Again we have the formula that
{Where v is the final velocity before hitting the ground.}
⇒
⇒ v = 65.96 feet / sec. (Answer)
You would answer this question using simultaneous equations, so if m is movies and v is video games, then:
9m + 7v = 65
3m + 5v = 37
9m + 7v = 65
9m + 15v = 111
(minus)
-8v = -46
÷ -8
v = $5.75
Then you can substitute the value of V in to find the value of m, so:
3m + (5 × 5.75) = 37
3m + 28.75 = 37
- 28.75
3m = 8.25
÷ 3
m = 2.75
So you get the answers as Video Games are $5.75 each and Movies are $2.75 each, I hope this helps!