GOAL Solve a two-dimensional projectile motion problem in which an object has an

Question

GOAL Solve a two-dimensional projectile motion problem in which an object has an initial Horizontal velocity. An Alaskan rescue plane drops a package of emergency rations to stranded hikers, as shown in Figure 3.19. The plane is traveling horizontally at 40.0 m/s at a height of 1.00 times 10^2 m above the ground. Neglect air resistance, (a) Where does the package strike the ground relative to the point at which it was released? (b) What are the horizontal and vertical components of the velocity of the package just before it hits the ground? (c) Find the angle of the impact. STRATEGY Here, we're just taking Equations 3.13 and 3.14, filling in known quantities, and solving for the remaining unknown quantities. Sketch the problem using a

Explanation / Answer

(A) package initially has only horizontal velocity.

v0x = 40 m/s

v0y = 0

vertical displacement as it hit the ground. y = - 100 m

Applying y = v0y t + ay t^2 / 2

- 100 = 0 - 9.81 t^2 / 2

t = 4.51 sec

distance travelled in horizontal.

x = 40 x 4.51 = 181 m

pakage is at distance = sqrt(181^2 + 100^2) = 207 m

at angle = tan^-1(100/181) = 29 deg below the horizontal.

(b) horizontal component = 40 m/s

vertcial component = 0 - (9.81 x 4.51) = - 44.2 m/s

Or 44.2 m/s downwards

(c) angle of impact = tan^-1(44.2 / 40)

= 48 deg below the horizontal.

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