# Physics

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We are standing at a distance d=15 m away from a house. The house wall is h=6 m high and the roof has an inclination angle β=30 ∘. We throw a stone with initial speed v0=20 m/s at an angle α= 42 ∘. The gravitational acceleration is g=10 m/s2

(a) At what horizontal distance from the house wall is the stone going to hit the roof - s in the figure-? (in meters)

(b) What time does it take the stone to reach the roof? (in seconds)

Help!!!!!

• Physics -

8.01 course ah?

• Physics -

did you manage to solve it

• Physics -

yes! Do you have an idea?

• Physics -

no but how did you get it?

• Physics -

@ PHYSICS I didn't get it!

• Physics -

The time to rich the highest point is
tₒ= 2vₒ•sinα/2g =2•20•sin35/2•10 =1.15 s
The time for covering the distance to the wall ‚d’ is
t₁=d/vₒ•cosα =15/20•cos35= 0.92 s
At horizontal distance d from the initial point the ball is at the height
h₁=vₒ•sinα•t₁ -gt₁²/2 =
=20•sin25•0.92 -10•0.92²/2 =6.31 m.
The highest position of the ball moving as projectile is
H= vₒ²•sin²α/2g =20²• sin²35/2•10 = 6.38 m.
Therefore, the ball meets the roof at its upward motion, =>
d+s=vₒ•cosα•t …..(1)
h+s•tanβ= vₒ•sinα•t - gt²/2 …..(2)
From (1)
s = vₒ•cosα•t -d
Substitute ‘s’ in (2)
h +tanβ(vₒ•cosα•t –d) =
=vₒ•sinα•t - gt²/2,

6+ 0.58(20•0.82•t -15) = 20•0.57•t- 5t²,

5t² -1.9t-2.7 =0
t=0.95 s.
s= vₒ•cosα•t –d=
=20•0.82•0.95 – 15=
=15.58 – 15 =0.58 m

• Physics -

@Elena thank you!I found t but s it's wrong

• Physics -

@Elena it works fine I found my mistake !thank you again

• Physics -

you are truly brilliant.

• Physics -

@ Anonymous what do you have for T and S?

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