6. A girl throws a rock southward from the top of a treehouse 30m above the grou

Question

6. A girl throws a rock southward from the top of a treehouse 30m above the ground, at a 60 angle and with an initial speed of 20 m/s. If the base of the tree is the origin (a) Find a formula for the position of the rock after t seconds (b) Find the coordinates of the point where the rock hits the ground. (c) How many seconds will pass before the rock hits the ground? 7. A ball with mass 0.8 kg is thrown southward into the air with a speed of 30 m/s at an angle of 30° to the ground. A west wind applies a steady force of 4 N to the bal in an easterly direction. Where does the ball land and with what speed? 5

Explanation / Answer

Solution:(7)

m = 0.8 kg, and 4 N = 4 kg*m/s2

Fx = max ==> 4 = 0.8ax ==> ax = 5 m/s2

a(t) = < 5, 0, -9.8>

V(t) = < 5t + Lx, Ly, -9.8t + Lz >

V(0) = < 0, 15?3, 15 >

V(t) = < 5t, 15?3, -9.8t +15 >

r(t) = < 5t2/2, 15?3 t, -4.9t2 + 15t >

rz = 0; ==> -4.9t2 + 15t = 0 ==> -t(4.9t - 15) = 0 ==> t = 15/4.9

r(15/4.9) = < 5*(15/4.9)2/2, 15?3 * (15/4.9), 0> = < 23.4277, 79.5329, 0 >

v(15/4.9) = < 5(15/4.9), 15?3, -9.8(15/4.9) +15 > = < 15.3061, 25.9808, -15>

To find out where the ball lands we use Pythagoras theorem;

S = ?{(23.4277)2 + (79.5329)2} = 82.9116 m

Similarly the instantaneous speed at that moment where the ball lands can be found by using;

?(Vx2 + Vy2 +Vz2 ) = ?{(15.3061)2 + (25.9808)2 + (-15)2 } = 33.679 m/s

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.