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daser333 [38]
3 years ago
6

A projectile is fired with muzzle speed 250 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe

s the projectile hit the ground and with what speed?
Mathematics
1 answer:
qaws [65]3 years ago
7 0

The projectile's horizontal and vertical positions at time t are given by

x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ\,t

y=30\,\mathrm m+\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ\,t-\dfrac g2t^2

where g=9.8\dfrac{\rm m}{\mathrm s^2}. Solve y=0 for the time t it takes for the projectile to reach the ground:

30+\dfrac{250}{\sqrt2}t-4.9t^2=0\implies t\approx36.2458\,\mathrm s

In this time, the projectile will have traveled horizontally a distance of

x=\dfrac{250\frac{\rm m}{\rm s}}{\sqrt2}(36.2458\,\mathrm s)\approx6400\,\mathrm m

The projectile's horizontal and vertical velocities are given by

v_x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ

v_y=\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ-gt

At the time the projectile hits the ground, its velocity vector has horizontal component approx. 176.77 m/s and vertical component approx. -178.43 m/s, which corresponds to a speed of about \sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}.

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Find the arc length of a 30 degree sector of a circle with a radius of 10 cm
Elena-2011 [213]
Arc length = Ф/360 * 2πr
= 30/360 * 2*3.14*10
= 1/12 * 62.8
= 5.23

In short, Your Answer would be 5.23 cm

Hope this helps!
3 0
3 years ago
What is the missing step in this proof? a. ∠abc ≅ ∠dbe b. ∠bca ≅ ∠bde c. ∠acb ≅ ∠deb d. ∠bde ≅ ∠ade e. ∠cab ≅ ∠dac
Nana76 [90]

Based on the reflexive property of congruency, the missing step in the proof is: A. ∠ABC ≅ ∠DBE

<h3>What is the Reflexive Property of Congruency?</h3>

The reflexive property of congruency states that an angle will always be congruent to itself.

In the diagram given, we can prove that ∠ABC ≅ ∠DBE based on the reflexive property.

Therefore, the missing step in nthe proof is: A. ∠ABC ≅ ∠DBE

Learn more about reflexive property on:

brainly.com/question/1601404

#SPJ4

5 0
2 years ago
Help pleaseee look at the photo above... What’s the answer for y?
Mashutka [201]

y = 25x

the x represents gallons

5 0
3 years ago
I need the correct answers help pls
Aleksandr [31]
The answer is -3x^2+18x-30
7 0
2 years ago
Through: (3,5), slope=5\3
ANEK [815]
So slope intercpet form
y=mx+b

m=slope
b=y intercpet


slope=5/3
in (x,y) form

x=3
y=5 is one point


subsitute and solve for b
y=mx+b
5=5/3 times 3+b
5=3/3 times 5+b
5=1 times 5+b
5=5+b
subtract 5 from both sides
0=b

equation is
y=5/3x+0 or
y=5/3x
3 0
3 years ago
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