Question

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Problem 7.5 A tank fires a round at a 30° angle with a muzzle velocity of 600 m/s. The round is expected to hit a mountainside one kilometer away. The mountainside also has an average angle of 30°. How far up the mountainside will the round be expected to travel before hitting the ground (d) if we ignore air resistance? (Solution: d = 5.37 km)

Answer 1

Answer'- Given that, Angle = 30° muzzle velocity 6o om/s. Griven figuse as shown below, 130° 1300 100om Неse, Ih hodizontal disecbion (no accelexabon and constant по velocity): l000 +dcos38 = (60o COS38)t loootd Cos30 t: b0oco5 30 In vestical disecbon(3oavity acbing downwards): )/loo0tdcos30° (dsin36) - (600 Sin 3000 cos 30 po00+das30) b0o(o530

asd= 577.35+0.5d -† (9-81)(1000)"+ (dca530);a(1000) (dcossa) (6oo cos36) 732.0508d) 0-5d= 577.3 5+0.5d- 4.905/10000004 0.75d+1732 270000 0.5d=577-35+0-5d - 18.167-1-3625x1058=0.0314656d --o5d+ 57:35tosd-18-167-1:3625 xió 0.0314656d 0: 577.35-18.167-1.3625 X10-5d 0.0314656d O = 559.183-1-3625x10582-0.0314656d. -> 1:362 5X105dto.0314656 d-559.183=0 d:-0.0314656 +Jc0.0314654)74(1:3625 X16)(s59483) 2(1:3625X105) d: -0:031465 6+ 0.1993853 2.725 X105 d = 0.145919 2.725 X105 d= 5355 m d= 5. 36KM