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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

qaws [65]

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 $\sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}$ .

7 0

3 years ago

1. When Lucas dumped the coins out of his piggy bank, he noticed that there were only nickels and dimes, and the number of nicke

vaieri [72.5K]

1- The total value of the Lucas coins dumped out of his piggy bank was $ 5.

2- Franco dumped out 36 coins from his piggy bank (16 quarters and 20 nickels).

3- There is no possible solution, as neither combination gives a total of $ 10, which is the combined total of Lucas and Franco's coins.

1- Given that when Lucas dumped the coins out of his piggy bank, he noticed that there were only nickels and dimes, and the number of nickels was twice the number of dimes, to determine, if there were 50 nickels, what was the total value of the Lucas coins dumped out of his piggy bank, the following calculation must be performed:

Nickel = 0.05
Dime = 0.10
N + D = X
N + 1 / 2N = X
50 + 25 = 75
50 x 0.05 + 25 x 0.1 = X
2.50 + 2.50 = X
5 = X

Therefore, the total value of the Lucas coins dumped out of his piggy bank was $ 5.

2- Since when Franco dumped the coins out of his piggy bank, he noticed that there were only nickels and quarters, and the number of quarters was six more than half the number of nickels, to determine, if the total value of the coins Franco and Lucas dumped out of each piggy bank was the same, how many coins did Franco dump out of his piggy bank, the following calculation must be performed:

Nickel = 0.05
Quarter = 0.25
Q = 2N + 6
4 x 0.25 + 6 x 0.25 = 1 + 1.5 = 2.5
8 x 0.05 = 0.40
2.5 + 0.4 = 2.9
8 x 0.25 + 6 x 0.25 = 2 + 1.5 = 3.5
16 x 0.05 = 0.8
3.5 + 0.8 = 4.3
10 x 0.25 + 6 x 0.25 = 2.5 + 1.5 = 4
20 x 0.05 = 1
4 + 1 = 5
10 + 6 + 20 = 36

Therefore, Franco dumped out 36 coins from his piggy bank (16 quarters and 20 nickels).

3- Since when Callie dumped the coins out of her piggy bank, she noticed that there were only nickels, dimes and quarters, and the number of dimes was one more than twice the number of quarters, and there were half as many quarters as nickels, y the coins dumped out of Callie's piggy bank had a total value equal to that of the coins dumped out of Franco's and Lucas' piggy banks combined, to determine what was the total value of the nickels and dimes dumped out of Callie's piggy bank, the following calculation should be performed: