Maths question help?! Motion and Integration (1 Viewer)

angel102 · Jul 23, 2016

Need help answering this question:

A projectile is accelerating at a constant rate of − 9.8 ms− 2. If it is initially 2 m high and has
a velocity of 4 ms− 1, find the equation of the height of the projectile.

Any answers will be appreciated thanks

Katebate · Jul 23, 2016

angel102 said:
Need help answering this question:

A projectile is accelerating at a constant rate of − 9.8 ms− 2. If it is initially 2 m high and has
a velocity of 4 ms− 1, find the equation of the height of the projectile.

Any answers will be appreciated thanks

Okay, it's late so please forgive me if I do this completely wrong, but it's worth a shot hey.

ÿ = -9.8

ẏ = -9.8t + C
when t = 0, ẏ = 4sintheta

therefore, C = 4sintheta

y = -4.9t^2 + 4tsintheta + C

C = 2 when t = 0

Therefore height = -4.9t^2 + 4tsintheta + 2 (hopefully)

ProdigyInspired · Jul 23, 2016

Is velocity considered as sin theta? Pretty sure thats physics.

$\begin{matrix} \begin{matrix} a\quad =\ddot { x } \end{matrix} \end{matrix}\\ \begin{matrix} \ddot { x } =-9.8\quad ms^{ -2 }\\ At\quad t\quad =\quad 0,\quad x\quad =\quad 2,\quad \dot { x } =\quad 4ms^{ -1 }\\ \dot { x } =\quad \int { \ddot { x } } =\quad -9.8t\quad +\quad C\\ Since\quad when\quad t\quad =\quad 0,\quad \dot { x } =\quad 4,\\ C\quad =\quad 4\\ \\ \therefore \quad \dot { x } =\quad -9.8t\quad +\quad 4 \end{matrix} \\ x,\quad which\quad =\quad height,\quad is\quad \int { \dot { x } } \\ \begin{matrix} \int { \dot { x } } =\quad -9.8t^{ 2 }\frac { 1 }{ 2 } +\quad 4t\quad +\quad C \\ Since\quad when\quad t\quad =\quad 0,\quad x\quad =\quad 2 \\ C\quad =\quad 2 \\ \therefore \quad x\quad =\quad -9.8t^{ 2 }\frac { 1 }{ 2 } +\quad 4t\quad +\quad 2\quad \end{matrix}$

angel102 · Jul 23, 2016

answer is -4.9t + 4t +2
thanks for your replies

leehuan · Jul 23, 2016

ProdigyInspired said:
Is velocity considered as sin theta? Pretty sure thats physics.

What do you mean by this? I recall that in maths what you assume are

$\ddot{x}=0\\ \ddot{y}=-g\\ \dot{x}|_{t=0}=V\cos \theta\\ \dot{y}|_{t=0}=V\sin\theta$

Maths question help?! Motion and Integration (1 Viewer)

angel102

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