Mathematics (1 Viewer)

[spotspot1]

The height of a projectile is given by h=7=6t-t^2, where height is in meters and time is in seconds.
a) Find the initial height.
b) find the maximum height reached
c) when will the projectile reach the ground?
d) sketch the graph showing the height of the projectile over time t.
e) How far will the projectile travel in the first 4 seconds?

Hey guys would you help me out by solving question e?
Answer are:
a) 7m
b)16m
c)after 7s
d)graph
e)10m

 

[integral95]

The height of a projectile is given by h=7=6t-t^2, where height is in meters and time is in seconds.
a) Find the initial height.
b) find the maximum height reached
c) when will the projectile reach the ground?
d) sketch the graph showing the height of the projectile over time t.
e) How far will the projectile travel in the first 4 seconds?

Hey guys would you help me out by solving question e?
Answer are:
a) 7m
b)16m
c)after 7s
d)graph
e)10m

I think you typed it wrong lol, is it a - or +?

 

[integral95]

and the last question is integrating the function with limits 0 to 4

 

[davidgoes4wce]

I reckon part (b) is a bit subjective, for the maximum height of 16 metres to occur, you have to have a time of -3 seconds, which is clearly unfeasible.

 

[davidgoes4wce]

yeah should the question be



or

?

 

[InteGrand]

I reckon part (b) is a bit subjective, for the maximum height of 16 metres to occur, you have to have a time of -3 seconds, which is clearly unfeasible.

The question was typo'ed I think, it was meant to be h = 7 + 6t – t² (a plus sign was written as =, which is an easy typo to make).

 

[InteGrand]

yeah should the question be



or

?

(The physical significance of the coefficient of the t term is that it is the initial vertical velocity.)

 

[spotspot1]

i did type it wrong, sorry for the confusion everyone !
The question is
h=7+6t-t^2

 

[davidgoes4wce]

Here is my worked out solution:



Part (d)



Part (e)

 

[spotspot1]

Thank you everyone for helping out!

 

[t-t]

(d) When t=3s, height=16m
When t=4s, height=15m

Since initial height is 7m,
16m-7m=9m
going back is 16-15=1m
9+1=10m

 

[pikachu975]

For maximum height reached would you need to test the nature of the stationary point or is that only for maxima minima questions?

 

[leehuan]

For maximum height reached would you need to test the nature of the stationary point or is that only for maxima minima questions?

You need to show that it's a maximum height and not a "minimum height" somehow

Some questions let you chance it but it's never a risk you should be taking - ignoring the test for nature

 

[InteGrand]

For maximum height reached would you need to test the nature of the stationary point or is that only for maxima minima questions?

You don't need to "test" anything here, you can just say that since h is a quadratic function of t with negative leading coefficient, the stationary point is a maximum.

Anyway, for this question, it sounds like they're letting you assume it's a maximum and are just asking for when this occurs.