AQ4.4: Activity Questions 4 - Not Graded

[Ayushi Gupta]

A stone is thrown with an initial speed uu (m/s) as shown in figure 3. The height of the stone’s trajectory above the ground is, H(t)=−5t2+12utH(t)=−5t2+12ut (here tt is the time of flight). If the highest point in air that the stone can reach is 5m above the ground, then calculate the initial speed u

https://backend.seek.onlinedegree.iitm.ac.in/20t1_ma1001/assets/img/W4aqn4.1.png  

 20 m/s

 10 m/s

 12m/s

  2 m/s

Can you please tell me how to solve this question

[Kaushal Patil]

Hi

Th trajectory of the stone being thrown is considered as a downward parabola with the quadratic equation mentioned in the question itself. Here the variable is t and u(INITIAL VELOCITY) is a constant. As it is a downward parabola, the value of the function H(t) will give it’s maximum value at the vertex point. But the maximum value of H is already known as 5 m. So by finding the vertex as t=-b/2a which gives value as t= U/20 or it can be put as u=20t.

So putting this value of u in the equation and given the value of H(t) maximum is 5m we get the equation after simplifying 10(t)^2 =10. So value of t is 1 (-1 isn’t an eligible value for time). Substituting t=1 in u=20t we get 

U=20 m/s 

[Sree Kavitha]

hi i still cant understand

[Sree Kavitha]

how do u get t=u/20

pl explain in detail . vry much stuck in this problem , unable to move on

On Tuesday, November 10, 2020 at 12:29:12 AM UTC+5:30 Kaushal Patil wrote:

[Malabika Guha Mustafi]

@sree,

H(t) [y is H(t)] =5 (max) when t(x is t here)is u/20 as you computed.

Put both the value in equation and compute u.

[Smiley Boy]

Here the solution

H(t) =  -5t^2 + (1/2)ut 

A= -5 And B= (1/2)u

t= -B/2A  

t = -(1/2)u / 2(-5)   = (u/2) / 10  

t= U/20 or U=20t

Max(H(t)) = 5 , U =20t

5 = -5t^2 +(1/2)20t (t)

5  = -5t^2+10t^2

5= 5t^2

t^2=1

t= + or - 1

commonly speed can't be ng so we take +1

U =(1)20

U= 20

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Thanks.!

Bala :)

[Satish]

thanks bro

[Aisha Siddiqa]

Axis of symmetry is calculated as -b/2a right. How did t=-b/20 ?