Question

(4 points) A stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r(t) = 4ti — 2tj + (24.5 – 4.912) k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up. (a) How high is the rooftop? meters. (b) When does the stone hit the ground? seconds. (the vector's magnitude is in (c) Enter a vector that indicates where the stone hits the ground: meters) (d) How fast is the stone moving when it hits the ground? meters per second

Answer 1

C Dans Given Hot 8 C+) = 478 - at: + (24.5 - 4.94")K Time (t) = 0 (a) 80of top height ko Comporеnt of 8 (0) 4.9 (0)² 24.5 =) 215-o 24°5 meters (b) the height of the Ko Component åct) stone hits the Joosend olen the K-. comporent Ô Ct) is equal to 'o' 24•5-4.9+² zo 4.942 =2405 +? = 24.5 4.9 Ł 5 Secu (0) 8 (5) = 49 5 Take ta 55 Store hits the ground in 155 205 + (quo5 - 4.9 (us) = 4051 - 95+ (24.5 - 409. (5)) k = 455i - 255i + (au•5-24.5k

meheer V(t) = doct) dt 485 i-2059 +0 = uusi-2055 ...The store hits the ground at K405, - 215, 0 07 (d) store velocity vector, at any ti me "is de (uti -8E5+ (au-5 – 4•9+2) k = 41-48 + (0-9.814)k V(t) = ui-29 - qu&tk Velocity of vector = V (J5) = 41-99-908 (3) k ui-gi-9.805 k hs the ground, the store travels at a speed 100g) - 742 +22+ (9-3 psy? Store 1674 +480.2 - w 500.2 = 99.365 29-36 msee